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\n
1. Introduction: culture in international business
\n
Biology and culture coevolve. The gene–environment coevolution has been established as foundational knowledge in different disciplines from language and cognitive studies [1, 2], social biology [3], sociology [4], philosophy [5] and systems theory/perspective of life that views all biological, cognitive, social aspects of human and animal behavior in an ecological dimension [6]. When it comes to human communication and social organization, the concept of organization ‘climate’ was discussed and studied mainly in the field of psychology in the early 1900s [7] where the authors spoke of ‘group norms’.
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International business (IB) and trade is part of a socio-biological human activity where communicating across cultures is increasingly inevitable. In that sense, IB is both an agent and recipient of cultural change [8] due to that IB and trade processes are inherently uncertain and evolving [9, 10], requiring a nuanced understanding of communication processes across cultures. With a large part of human activities being involved in daily transactions and exchange as a means of living, today’s economic theories, developed in an era of energy and material wealth from the 1800s onwards, is today largely out of sync with advancements in digitalization, climate change, biodiversity loss and rising social inequality [11, 12]. What is needed in address to global challenges is for a change in collective thinking and belief, i.e. a change in our culture, the way we communicate between ourselves and our environment, and how we conceive to manage our global resources as part of our daily transactions.
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Because of our evolving business environments, there has been an interest in scholastic literature since the late 1990s, for new perspectives in the study of culture in the field that includes communicating across cultures in trade negotiations [13], cultural dynamics in goods and services consumption such as what constitutes as luxury foods [14, 15, 16], culture in organization behavior and applications of the cultural dimensions construct to the study of culture [17, 18, 19, 20, 21, 22, 23].
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This chapter contributes to the current debate on how to frame future studies of a relative concept such as culture. It begins with giving a synopsis of the current paradigm of research methodology of the study of culture within IB, going on to address the two research questions of:
How and what can the field of IB studies gain with a broader definition and perspective of culture through a systems perspective? And,
Is there a means to operationalize a systems perspective framework to the study of culture (and thus the processes of communicating across cultures) within IB?
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1.1 Current research paradigm of culture within international business studies
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The discourse of organization culture in the field of international business (IB) began around the late 1970s with the work of Geert Hofstede [24, 25, 26]. In the 1950s, ‘cultural ecology’ was a focal concept in anthropology, evolving in response to the natural environment [27] anchored in the context of social life [28]. Culture was studied as an adaptive system with ecological and ideational dimensions [29].
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As culture and communication processes are intricate features of groups of individuals and manifests itself on various dimensions and levels of society, it is not an easy concept to decipher or measure [30, 31]. This challenge is further compounded today by advancing developments in information communication technologies (ICTs) that are digitally enabled. Digital infrastructures, wireless technology and social media platforms on the Internet for example, allow for the forming of virtual groups with instant contact that further blur concrete geographic boundaries of groups of individuals. It is these developments in technology coupled with the continued divergent views on the concept and definition of ‘culture’ that has proved to be one of IB’s biggest challenges. Already in 1952, Kroeber and Kluckhohn [32] had uncovered 164 definitions of ‘culture’, with their own being classified by Allaire and Firsirotu’s ([33]; p. 196) as “historical diffusionist” under culture as a “sociocultural system” though personally, their definition of culture that considers patterns of behavior and ideas reflects too, an acknowledgement of culture as a product of the mind through shared meanings and symbols:
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“Culture consists of patterns, explicit and implicit, of and for behavior acquired and transmitted by symbols, constituting the distinctive achievements of human groups, including their embodiments in artifacts; the essential core of culture consists of traditional (i.e. historically derived and selected) ideas and especially their attached values; culture systems may, on the one hand, be considered as products of action, and on the other as conditioning elements of further action.” ([32]; p. 357).
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Today there would be more definitions to contend with [34], as expressed by anthropologist Hall ([35]; p. 210), “I have come to the conclusion that the analysis of culture could be likened to the task of identifying mushrooms. Because of the nature of the mushrooms, no two experts describe them in precisely the same way, which creates a problem for the rest of us when we are trying to decide whether the specimen in our hands is edible.”
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Perhaps in address to the myriad definitions of culture, IB literature from the 1980s onwards suggests that culture has been investigated in a form that could be explicitly measured. The methodology is based on Hofstede’s cultural dimensions/distance (CD) construct that measures how distant cultures are when compared against certain constructs such as power distance, individualism vs. collectivism, uncertainty avoidance, masculinity vs. femininity and long-term vs. short-term orientation for relations [36, 37, 38, 39, 40, 41, 42, 43]. The effect of the CD construct was to provide the field with knowledge of culture that is mostly delineated by geographic region with a tendency toward average cultural values with an ‘either/or’ perspective that dichotomized similarities and differences between nationalities. Current global challenges today however, puts pressing need on a redefinition of culture study frameworks where culture needs to be understood from a systems network perspective.
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2. Culture in the context of systems theory
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In the Hofstedian CD construct, the notion of values is intricately tied to the radius of national culture that is operationalized in the cultural dimensions construct of culture applied to organization and management, to which culture is defined as “the collective programming of the mind which distinguishes the members of one category of people from those of another” ([25]; p. 389). There are however, complementary alternative views of how culture can be studied:
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“National identities are not predetermined. They emerge at particular points in time, under specific circumstances, … according to ‘a standard plot’ (Ting, 2008; p. 463), and these regularities form a basis for comparison of otherwise disparate cases (Laponce, 2008)” ([43]; p. 146).
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There has also been a suggestion that culture can be studied at different levels, using several frames of references, from geographical territorial boundaries and regions [44] to global cultural flows [45], whilst others advocate a multiple culture perspective that beyond the national and regional, also included organizational and professional cultures [22].
\n\n
“Obviously, we can study culture at different levels, just as we can adjust the focus of a camera to account for a large landscape or a small detail. Cultural analysis may result in a more or less fine-grained picture, every succeeding focus bringing additional information. The challenge is to define at each level a consistent approach to culture, which may account for what is shared and what is not.” ([46]; p. 170).
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Chevrier’s idea that it is varying sizes of groups of individuals who make up these levels, seem to run parallel to the life’s work of American psychologist Graves on his theory of human psychological development and stages of maturity he entitled the Emerging Cyclical Level of Existence Theory (ECLET). ECLET defines a value system that depends upon the interaction of two entities, (i) the socio-environmental context that Graves labels A, B, C, D, E, F, to A’ and N′ etc. and (ii) the neuropsychological capacities of the organism (individual, group or organization) to cope with (i) that Graves labels N, O, P, Q, R, S, to N′ and O′.
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The aspects of (i) when interacting in combination with (ii) produce the 8 systems of values and levels of existence that Graves labels AN, BO, CP, to A’N′ and N’O’. These systems of values and levels of existence provides a varying radius of framework as a way for man to conceptualize reality, consolidate their set of beliefs and corresponding behavior. These value systems can be found both at individual and group/national/regional levels. The Gravesian model is emergent, developing in an oscillating fashion in a double-helical structure (Figure 1). It illustrates socio-cognitive behavior in a systems-level approach to understanding culture and values. The level of existence model by Graves postulates that a level of living circumstance once stabilized over a period will tend to create its own existential problems to be solved, so that a next level of existence is necessarily sought for:
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Figure 1.
A double helix representation adapted from Graves [47; p. 187, 48] of the emergent development of the human psychosocial, existential states with potential development/evolution into more mature levels of existence and regression in times of socio-ecological challenges.
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“Overall, psychosocial development can indeed be seen as a complex wave-like phenomenon. But development does not occur in the smooth and flowing manner [but rather in] more a spurt-like, plateau-like, more a progressive, steady state, regressive movement in which certain demarcation points can be identified in the flowing process.”—Graves ([47]; p. 178)
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Figure 1 shows a double helical representation by Graves of the oscillating, spiraling development of the human psychosocial existential states. The value systems develop in a fixed order, though there can be progression or regression within this order. The space in between the areas within the two lines created by the alternating spurt and plateau of development phases, indicate increasing degrees of conceptual space. Each developing space on the spiral is larger than the one prior, developing in entropic fashion, in an emergent, open-ended system.
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Table 1 shows the value systems in brief with its corresponding labels and resulting problems of existence. The information in Table 1 and its levels of existence do not represent pure characteristics in which individuals can be pigeonholed neatly even if evolution occurs in an ordered hierarchy. Newer, higher level systems necessarily subsume lower level ones. Within this model, an element of regression is accounted for. Individuals/groups when confronted with a problem to be solved, may wish to withdraw into their ‘comfort zones’. Once realizing that this comfort zone no longer exists and when faced with increasing problems, they are then coerced into finding new solutions that thus push themselves into greater heights of the evolutionary double-helical structure of maturation and growth. As such, each value system is necessarily associated with a specific perspective of reality or ‘world-view’, thus generating multiple truths/cultures. The Gravesian model is useful because it points toward a generic model of human biological socio-cognitive development, where similar values can be mapped across national geographical boundaries. This lends a broader, more encompassing manner in which to understand how humans manage resources and live together. The individual being a unique and complex biological organism can be described to have layers upon layers of level building as they mature from the Automatic (AN) core, upwards and outwards in entropic fashion. The successive layers are not uniform, but rather they are flexible, dynamic and flow under various biological and contextual stresses as the individual reacts and relegates behavior in their own spacetime accordingly. Graves likened the individual’s evolution and maturing psychology as a “wrinkled plastic onion”, with layers of various flexible thicknesses that undergo continuous adjustment depending on perspective, frame-of-mind and surrounding context.
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Level of existence (LE)
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Existential state
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Nature of existence
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Description of existential state
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Problems of existence
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LE 8 Second being
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B’O’
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Experientialistic
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A new order of ‘we’ and ‘us’ is understood; the Self sees all elements as interconnected; a recognition of interdependence in the System
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Accepting existential dichotomies, and entropic relativities
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LE 7 First being
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A’N′
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Cognitivistic
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Return in new and higher order form to new survival problems in an age of scarcity; focus on reorganizing for interdependent existence
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Restoring viability to a disordered world
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LE 6
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FS
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Personalistic
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Equal trade sacrifice with a focus on the Inner Self that cooperates with Others; an understanding of cooperation
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Living with the human element
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LE 5
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ER
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Materialistic
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Focuses on the Outer Self of expressing things in the interest of one’s Self; pretense that what is of interest to Self is also in the interest of Others
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Conquering the physical universe to overcome want
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LE 4
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DQ
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Differentialistic
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Faith in authority; sacrifice Self for others; postponement of reward; focus on Inner Self
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Achieving everlasting peace of mind
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LE 3
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CP
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Egocentric
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Self is all important at cost of Others; need to control the external world
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Living with self-awareness
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LE 2
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BO
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Tribalistic
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Self-subsumed in Others; sacrifice to clan and survival of clan is important; focus is on the control of the Inner world
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Achievement of clan safety
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LE 1
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AN
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Automatic
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Survival on automatic basis; no awareness of Self or Others; no differentiation of Outer and Inner world
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Maintaining physiological stability
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Table 1.
An adaptation of Graves’ levels of existence and their corresponding existential states from Cowan and Todorovic ([47]; p. 169).
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Connecting knowledge across disciplines, the Gravesian system of levels of existence in the field of socio-cognitive science has related concepts from the field of quantum theoretical physics, that of (i) Niels Bohr’s “phenomenon” and (ii) Werner Heisenberg’s uncertainty principle illustrated in “wave-particle” duality. Bohr’s ‘phenomenon’ refers to that no elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon. This, Bohr had raised in his years of friendship with Albert Einstein when Einstein was at Princeton between the 1930s and 1950s. At the beginning, Einstein was none too comfortable with the concept of quantum physics and tried to show that quantum physics was incompatible with any form of reasonable understanding of reality, to which Bohr’s reply in brief was that Einstein’s concept of reality was too limited ([49]; p. 182). Bohr maintained that “what answer we get depends on the question we put, the experiment we arrange, the registering device we choose. We are inescapably involved in bringing about that which appears to be happening.” ([49]; p. 184).
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Heisenberg’s uncertainty principle has historically been confused with the “observer effect” which notes that measurements of any system cannot be made without affecting the systems. While Heisenberg offered that account at a quantum level as an explanation to quantum uncertainty, what should be highlighted is that the uncertainty principle is inherent in the properties of all wave-like systems where in quantum mechanics, all objects possess at the same time, a matter wave or wave-particle nature. Thus, the uncertainty principle in effect states a fundamental property of quantum systems and it is not about the observational interferences from the observer toward the system. All particles have at the same time, wave qualities, regardless of observation. In that sense, it is nonsensical to discuss the precise location of a wave on a string because particles do not have perfectly precise positions; just as likewise nonsensical to discuss the wavelength of a “pulse” wave traveling down a string since particles do not have perfectly precise momenta. When a position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength and thus momentum. Conversely, when momentum and thus wavelength is relatively well defined, the wave looks long and sinusoidal and therefore it has a very ill-defined position.
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The study of culture and communication strategies within the field of IB has thus far been delineated in relation to a collected set of values that belong to a group of individuals which tends to discount that individuals can behave and communicate differently in different groups and contextual settings. If we combined the perspectives of Bohr’s “phenomenon” and Heisenberg’s uncertainty principle with Graves’ levels of existence and human development, culture and how humans communicate with each other and their surrounding environment can be studied in relativity. Culture and communication processes can be viewed as dialogic processes between Individual and Group, each would define and perpetuate the other without which, neither would exist.
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Since values, motivation and beliefs define the individual and thus a group of individuals who share the same values and manners of communication, then these same levels of existence or system values necessarily go across borders, where the borders remain ill-defined (similar to Heisenberg’s uncertainty principle and in address to Hofstede’s micro-level analysis of cultures reflected in Table 2), defined only in relation to the observation point in relation to a specific purpose (similar to Bohr’s “phenomenon”). As such, the concept of culture and communication processes reflect both Individual and Group at the same time, the measurement of similarities or differences between the people of different groups of cultures defined only in relation to point and purpose of observation.
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Unit/level of analysis
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Purpose of analysis
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Goals of analysis
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Research strategy/design outcomes
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Group
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To investigate/understand micro-level variables across societies
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1. Prove universality of micro-level laws
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Culture is viewed as a black box with need to define micro-variables. Could be too complex to be fully explained. Vulnerable to ethnocentricity
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Group
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To investigate/understand micro-level variables within societies
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2. Illustrate uniqueness of each group/society
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Culture is viewed as a black box with too many variables lacking specificity. Polycentric perspective
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Society
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Concerned with ecological variables between societies. Focus on similarities/differences between societies
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3. Determine types of subsets of societies
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Culture specified in cultural dimensions construct. Polycentric perspective
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Society
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Concerned with ecological variables between societies. Focus on similarities/differences between societies
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4. Determine dimensions of societies and macro-level laws
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Culture specified in cultural dimensions construct. Geocentric perspective
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Table 2.
Adapted from Hofstede’s Culture’s Consequences ([24]; p. 35).
Four available research strategies with their goals numbered 1–4 for comparative multisociety studies, and the advantages/disadvantages of the research design outcomes.
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The conceptualization of culture and manners of communication within such a framework of systems theory drawn from the fields of quantum physics, socio-cognitive science/psychology and IB, depending point of observation of the phenomena, seemingly draws together the two dominant metaphors of culture in IB, as that of the layers of an ‘onion’ [50] and as that of the ‘ocean’ [51, 52, 53, 54]. Within this system perspective framework, culture and communication processes can be studied as inherently emergent.
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2.1 Conceptualizing culture beyond the cultural dimensions construct
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In critique of the CD construct, the metaphor of culture as an ‘ocean’ was proposed by Fang [51, 54]. Fang proposed a switch from Hofstede’s metaphor of culture as “onion” to “ocean” to “propose an alternative approach to the study of national cultures and international cross-cultural management in the era of globalization” ([51]; p. 72). The “onion” metaphor used by Hofstede [50, 55] illustrates how culture can be viewed as layers. These different layers of characteristics can be learned through teaching and practice, and can be displayed by rituals, in admiration of heroes (both real and fictive) and through (status/material) symbols. These outer manifestations, of layers of culture radiate from and surround a somewhat stable and defined core of the ‘onion’ that are the basic socio-cultural values that is what people tend to believe things ‘ought to be’, where in accordance of culture as a programming of the mind, Hofstede argued that by age 10, most children would have had their basic values in place, set with their foundation orientation toward society’s dominant ideology. Fang saw the “onion” metaphor as “a product of the cold war era during which national cultures were like “black boxes” (self-contained, tangible and rigid “onions”). Few cultures knew what other cultures were thinking and doing.” ([51]; p. 84) But in the era of globalization, he felt that a better metaphor would be to view culture, with all its inherent paradoxes and internal variations, as an “ocean”, where the ocean “has no boundaries, and its various waters are both separate and shared, both different and similar, and both independent and dependent” ([51]; p. 88).
\n
Uncomfortable with the “functionalist” [56, 57] and “deterministic” [20] paradigm that seeks objectivity, measurement and prediction, Fang felt that research frameworks in IB had philosophical foundations heavily influenced by Karl Popper’s “analytical logic” that continued to encourage the tradition in literature of a bipolarized perspective of culture with “either/or” dimensions. He preferred instead, “a dialectical approach that sees each national culture as having a life of its own full of dynamics and paradoxes” ([51]; pp. 71–72) where an eastern ‘dualities’ approach to culture theory with a “both/and” perspective would be more useful considering today’s global challenges and changing business environments.
\n
\n
\n
\n
3. Revisiting research strategies and frameworks of analysis
\n
The previous sections addressed the first research question posed in this chapter. By incorporating perspectives from other disciplines (social biology, physics and psychology) on how culture is studied, the field of IB can move toward a systems theory understanding of culture and communication processes in address to global challenges and changing business environments.
\n
Comparative studies of organizations inherently favor a binary approach to what is being studied [24, 58]. In address to the second research question, one way of beginning to operationalize a systems perspective to culture and communication processes is to revisit the foundations of the CD construct reflected in Hofstede’s Figure 1.6 ([24]; p. 43) shown in Table 2, where Hofstede illustrates four types of research strategies and their goals (numbered 1–4 in Table 2) for studying universal and specific characteristics of culture at different levels of analysis.
\n
Cells 1 and 2 are studies that focus on either similarities or differences among and between groups in societies. These studies are concerned with micro-level variables and their relationship, meant to be measured both within and across different societies. Cell 1 studies try to prove the universality of micro-level laws with a nomothetic-etic orientation [59], whilst Cell 2 studies are more idiographic-emic where showing the differences among societies also means showing the uniqueness of each [60]. Hofstede argues that studies in Cells 1 and 2 can go across cultures [61, 62] but do not necessarily specify what “culture” stands for, thereby likening it to a “black box”, else stating that it is set against a “culture-free context”. Micro-level group studies can also go across cultures by comparison of the average scores of each group. This he acknowledged is problematic since in the broader sense of research strategy, the variables considered may be too many to be known and too complex to be fully understood. These uncertainties thus contribute to inaccurate measurements and difficulties in operationalizing a research framework that can be applied to practical use.
\n
Cells 3 and 4 are studies that focus on either similarities or differences among societies based on “ecological variables and their relationships” measured at the level of societies. In Cell 3, subsets of cultures are studied in relation to others similar among themselves but differ from other types or subsets [63, 64, 65]. Hofstede recognizes Cell 4 studies, as “geocentric” in nature, whereas Cells 2 and 3 are “polycentric” and Cell 1 studies as “ethnocentric”. Cell 4 research strategies would be comprehensive enough to cover various geographical regions, with the assumption that focusing on differences will also highlight similarities between societies/nations and regions.
\n
Still, in this debate is the recognition that studies situated in their own respective Cells are seldom, if ever, provide an adequate overview of the study of cultures per se, where Hofstede deemed it positive to have studies situated across all Cells with the results thereafter compared, where the approach to the study of culture and organization should not just be multidisciplinary but multi-leveled. In his pioneering efforts, Hofstede [24] lends examples to studies situated in all four cells, clearly defining that his own efforts with IBM and the formulation of cultural dimensions as belonging to studies “concerned with determining dimensions of societies and laws at the level of societal variables” ([24]; p. 43).
\n
\n
\n
4. Operationalizing research strategies for the study of culture from a systems perspective
\n
Viewed from an integrated systems perspective, Table 3 illustrates how studies an be done in each quadrant whilst scholars even when using different approaches to the study of culture and communication processes, would continue to cross-reference the works of colleagues both within and across disciplines to gain broader insights into culture, communication and eco-organization management. The main difference between the research strategies perspective in Tables 2 and 3 is that studies in Cell 2 in Table 3 allows for a re-formulating of the current cultural studies framework that take into consideration how culture and communication processes are studied in other disciplines. The resulting framework to the analysis of culture for studies in Cell 2 of Table 3 can be approached by using both quantitative and qualitative methods.
\n
\n
\n
\n
\n\n
\n
\n
Within groups/constellations
\n
Across groups/constellations
\n
\n\n\n
\n
Concerned with micro-level variables
\n
1. Determine types of subsets of societies
\n
2. Determine global values, including in virtual spaces
\n
\n
\n
Concerned with macro-level variables
\n
3. Illustrate uniqueness of each group/constellation
\n
4. Determine cultural dimensions of group/constellation
\n
\n\n
Table 3.
Reworking the framework to research strategies for comparative studies on culture, communication processes and organization at micro and macro levels, within and across national boundaries, in the era of globalization.
\n
Using the research strategies outlined in Table 3, the previous works of other outstanding scholars in the field of cultural studies that began in the 1930s with studies in cultural anthropology in relation to organization [66, 67, 68, 69, 70].
\n
To this end, both Hofstede’s CD construct and Fang’s Yin Yang approach provide a platform toward a larger integral system of studying culture. The CD construct provides neatened frameworks for cultural averages to be studied and the eastern dualism approach provides for an overarching theoretical framework to explain the anomalies within the CD paradigm. Considering current global challenges and an increasing inequality, humans from various regions and parts of the globe will need to increasingly learn to co-exist and co-evolve with the ecological dimension.
\n
\n
\n
5. Reflections, limitations and conclusion
\n
Current research strategies of studying culture and communication processes that bolster dominant economic theories within the field of IB seems inadequate in addressing challenges faced by evolving business environment and global challenges, from the management of the global resources to the management of our ecology. The purpose of this chapter is to contribute to the debate on finding means toward an integrated systems approach in culture theories toward an assimilated co-existence with remaining global resources and ecology where IB and trade makes up a large part of human living and management.
\n
In address to the first research question posed in this chapter, this study works with the assumption that international business and trade are inherent human activities that constitute a large part of living, managing and co-evolving with other global systems. The field of IB can work toward a system-network understanding of culture and communicating across cultures for IB studies by incorporating perspectives of culture and communication processes as studied in the fields of social-biology, quantum theoretical physics and psychology.
\n
In address to the second research question, operationalizing a systems perspective to culture and communicating across cultures, would require a revisit of current research strategies of culture in studies as applied to the field of IB and organization management. It is the Gravesian perspective of the evolution of human psychological maturity (that extends to groups, companies and societies) and levels of existence set within the context of the fundamental theoretical points of quantum physics—Heisenberg’s uncertainty principle and Bohr’s “phenomenon”—that can help define a concept of culture and manners of communication that go across geographical boundaries. The triangulation of theoretical perspectives from these different fields enables an explanation where perspective and point of observation is important in defining the radius of culture and communication strategies. Both Individual and Group are dialectically related in defining group culture and their communication processes, where one would not exist without the other.
\n
Addressing global challenges from rapid climate change, biodiversity loss and rising social inequality in a context of uncertainty and changing business environments lend increasing pressure to understand and study culture and human-ecology communication processes from a systems perspective. Understanding cultural values across geographical boundaries and what we today would call a miscommunication between cultures due to cultural friction could be re-perspectivized as differences in levels of socio-cognitive and ecological maturity development, rather than as differences in national cultures and identities. There is after all, only one globe in which we are all a part.
\n
\n\n',keywords:"global challenges, culture collective behavior, communication management, international business, research methodology, system theory",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/64461.pdf",chapterXML:"https://mts.intechopen.com/source/xml/64461.xml",downloadPdfUrl:"/chapter/pdf-download/64461",previewPdfUrl:"/chapter/pdf-preview/64461",totalDownloads:537,totalViews:204,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"April 30th 2018",dateReviewed:"October 22nd 2018",datePrePublished:"November 20th 2018",datePublished:null,dateFinished:null,readingETA:"0",abstract:"Biology and culture co-evolve, affecting collective social behaviors in the way we interact with others and with our environment. The working assumption in this study is that biology and culture provide the environment in which individuals interact/communicate. Human communication is thus both created and circumscribed by culture. Cultural values differ between different groups of individuals. This relativity in culture is illustrated by various social artifacts and resulting differences in socio-communicative behaviors that often leads to miscommunication between individuals of different cultures. This inherent relativity of culture has also posed a methodological challenge for researchers who study culture and thus communication management, particularly within the field of international business (IB) studies, where transactional behavior makes up for much of human behavior. Global challenges and a changing business environment due to converging technological platforms place increasing pressure on the need to revisit the cultural dimensions construct. The aim of this chapter is to give readers an overview of current frameworks of how culture is studied within the field of IB and how this perspective can be broadened with ideas drawn from other disciplines including social-biology, quantum theoretical physics and psychology. It revisits current culture research strategies and suggests a model in which relativity in culture can be addressed through a systems perspective of research.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/64461",risUrl:"/chapter/ris/64461",book:{slug:"a-complex-systems-perspective-of-communication-from-cells-to-societies"},signatures:"Cheryl Marie Cordeiro",authors:null,sections:[{id:"sec_1",title:"1. Introduction: culture in international business",level:"1"},{id:"sec_1_2",title:"1.1 Current research paradigm of culture within international business studies",level:"2"},{id:"sec_3",title:"2. Culture in the context of systems theory",level:"1"},{id:"sec_3_2",title:"2.1 Conceptualizing culture beyond the cultural dimensions construct",level:"2"},{id:"sec_5",title:"3. Revisiting research strategies and frameworks of analysis",level:"1"},{id:"sec_6",title:"4. Operationalizing research strategies for the study of culture from a systems perspective",level:"1"},{id:"sec_7",title:"5. Reflections, limitations and conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Everaert M, Bolhuis J. The biology of language. Neuroscience and Biobehavioral Reviews. 2017;81(Pt B):99-102\n'},{id:"B2",body:'Brothers L. The social brain: A project for integrating primate behaviour and neurophysiology in a new domain. Concepts in Neuroscience. 1990;1:27-51\n'},{id:"B3",body:'Carr-Saunders AM. The Biological Basis of Human Nature. London: Oxford University Press; 1942\n'},{id:"B4",body:'Rose N. The human sciences in a biological age. 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Gothenburg, Sweden: University of Gothenburg; 2009\n'},{id:"B64",body:'Russet BM. Delineating international regions. In: Singer JD, editor. Quantitative International Politics: Insights and Evidence. New York: Free Press; 1968\n'},{id:"B65",body:'Adelman I, Morris CT. Society, Politics and Economic Development: A Quantitative Approach. Baltimore: Johns Hopkins University Press; 1967\n'},{id:"B66",body:'Mayo E. The Human Problems of an Industrial Civilization. New York: Macmillan; 1933\n'},{id:"B67",body:'Roethlisberger FJ, Dickson WJ. Management and the Worker: An Account of a Research Program Conducted by a Western Electric Company, Hawthorne Works, Chicago. Cambridge, MA: Harvard University Press; 1939\n'},{id:"B68",body:'Gardner B. Human Relations in Industry. Homewood, III: Irwin; 1945\n'},{id:"B69",body:'Warner WL, Low J. The Social System of the Modern Factory: The Strike, a Social Analysis. New Haven, Conn: Yale University Press; 1947\n'},{id:"B70",body:'Richardson F, Walker C. Human Relations in an Expanding Company. New Haven, Conn: Yale University Press; 1948\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Cheryl Marie Cordeiro",address:"cheryl.cordeiro@nofima.no",affiliation:'
The Norwegian Institute of Food, Fisheries and Aquaculture Research (NOFIMA), Tromsø, Norway
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\n
1. Introduction
\n
Bitcoin is a digital currency built on a peer-to-peer network and on the blockchain, a public ledger where all transactions are recorded and made available to all nodes. Opposite to traditional banking transactions, based on trust for counterparty, Bitcoin relies on cryptography and on a consensus protocol for the network. The entire system is founded on an open source software created in 2009 by a computer scientist known under the pseudonym Satoshi Nakamoto, whose identity is still unknown (see [1]). Hence, Bitcoin is an independent digital currency, not subject to the control of central authorities and without inflation; furthermore, transactions in the network are pseudonymous and irreversible.
\n
Bitcoin and the underlying blockchain technology have gained much attention in the last few years. Research on Bitcoin often deals with cybersecurity and legitimacy issues such as the analysis of double spending possibilities and other cyber-threats; recently, high returns and volatility have attracted research toward the analysis of Bitcoin price efficiency as well as its dynamics (see, among others, [2, 3, 4]). Moreover, many contributions claim that Bitcoin price is driven by attention or sentiment about the Bitcoin system itself; see [5, 6, 7, 8]. Possible driving factors for the sentiment about the Bitcoin system are the volume of Google searches or Wikipedia requests as in [5], or more traditional indicators as the number or volume of transactions, as suggested in [6]. In [9], the author suggests a time series model in order to identify the dynamic relation between speculation activity and price.
\n
In this chapter, after having introduced the basic concepts underlying Bitcoin, we sum up and describe to a broader audience the recent outcomes of the research reported in [10], by avoiding unnecessary technicalities. Some new insights are also given by looking at possible extensions in order to take into account the presence of bubble effects or the special feature of Bitcoin being traded in different online platforms (exchanges) that will be further investigated in our future research.
\n
\n
\n
2. The Bitcoin network
\n
We recall that Bitcoin was first introduced as an electronic payment system between peers by Satoshi Nakamoto (pseudonym) in [1]. Opposite to traditional transactions, which are based on the trust in financial intermediaries, this system relies on the network, on the fixed rules and on cryptography. Bitcoins can be purchased on appropriate websites that allow to change usual currencies in the cryptocurrency.
\n
The Bitcoin network has several attractive properties for its users:
No central bank authority for money supply and no regulator;
Transactions are 24/7 and without any country border;
Transaction cost are almost negligible with respect to traded amount;
Transaction are anonymous;
The security of each transaction is guaranteed by cryptography and digital signature;
The security of the whole network is guaranteed by construction unless more than 50% of the network nodes agree on a deceptive action.
\n
As a digital payment system, Bitcoins may be used to pay for several online services and goods. Special applications have been designed for smartphones and tablets for transactions in Bitcoins and some ATMs have appeared all over the world (see Coin ATM radar) to change traditional currencies in Bitcoins. Accepting Bitcoins as a payment method is also related to an advertisement opportunity for companies. However, the high returns achieved in the last few years have transformed Bitcoin in a speculative asset affecting its use as a form of payment.
\n
The Bitcoin system has been subject to many cracks but has proven to be very resilient as the value of the cryptocurrency was able to rise again after all the falls. Nevertheless, at the time of writing, Bitcoin was experiencing a fall in its exchange rate with main fiat currencies.
\n
Two of the main crackdowns were China enforcement in December 2013 and Mt. Gox bankruptcy in February 2014.
\n
Besides technical and regulation issues, the Bitcoin system also faces reputational concerns.
\n
In fact, the ambiguity of anonymous transactions has blamed the network of allowing several criminal activities such as buying illegal goods, money laundering or the financing of terrorism actions. As a representative example, we recall that The Silk Road was a website that started selling narcotics and illegal drugs in 2011, payable in Bitcoins. The website was finally shutdown by 2013 and the owner was arrested and sentenced to life in prison. Again, anonymous transactions make it possible to use huge quantities of money, exchanged in Bitcoins, without declaring its origin, hence allowing for possible money laundering. However, according to a research performed by the UK government, the highest score related to money laundering is still cash, followed by the bank, accountancy and legal service providers (see https://www.gov.uk/government/publications/uk-national-risk-assessment-of-money-laundering-and-terrorist-financing).
\n
It is worth noticing that while counterparties are represented by secret addresses and are anonymous, all transactions are recorded and might be traced. Investigation is hence favored by this feature of the network.
\n
Despite the flaws in the system, Bitcoin has achieved a notwithstanding rise in recent years.
\n
In Figure 1, we report Bitcoin price and returns from January 2012 to December 2017 (source https://blockchain.info/en/charts).
\n
Figure 1.
Bitcoin price (top) and returns (bottom) from January 2012 to December 2017.
\n
\n
\n
3. An attention-based model
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The model we suggest in what follows is motivated by findings in [5, 6, 8, 11] where it is showed that Bitcoin price is related to investors’ attention measured by the trading volume and/or the number of searches in engines such as Google and Wikipedia. Bitcoin is treated as a financial stock as suggested in [12] and the suggested model may be applied in principle to other assets that are proven to depend on market attention.
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3.1. The model specification
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Consider a probability space \n\n\nΩ\nF\nP\n\n\n endowed with a filtration \n\nF\n=\n\n\nF\nt\n\n\nt\n≥\n0\n\n\n\n satisfying usual assumptions of right continuity and completeness.
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Let us denote the Bitcoin price process as \n\nS\n=\n\n\nS\nt\n\n\nt\n≥\n0\n\n\n\n and assume that it depends on an attention factor denoted by \n\nA\n=\n\n\nA\nt\n\n\nt\n≥\n0\n\n\n\n. The dynamics of the two processes are described by the following equation:
where \n\n\nμ\nA\n\n,\n\nμ\nS\n\n,\n\nσ\nA\n\n>\n0\n,\n\nσ\nS\n\n>\n0\n\n are constant parameters and \n\n\nW\nZ\n\n=\n\n\n\nW\nt\n\n\nZ\nt\n\n\n\nt\n≥\n0\n\n\n\n is an \n\n\nF\nP\n\n\n-standard Brownian motion in \n\n\nR\n2\n\n\n. Assume that \n\n\nF\nt\n\n=\nσ\n\n\nW\nu\n\n\nZ\nu\n\n\nu\n≤\nt\n\n\n,\n\n for each \n\nt\n≥\n0\n.\n\n
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It is well known that the above dynamics for the attention factor is a geometric Brownian motion, the solution of which is given by \n\n\nA\nt\n\n=\n\nA\n0\n\n\nexp\n\n\n\n\n\nμ\nA\n\n−\n\n\n\nσ\nA\n\n2\n\n2\n\n\n\nt\n+\n\nσ\nA\n\n\nZ\nt\n\n\n\n\n for \n\nt\n≥\n0\n\n which has a log-normal distribution; integrating the price process is straightforward to get
We collect in this subsection the properties of the logarithmic returns obtained by the price process defined in Eq. (1).
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Consider the discrete process \n\n\n\n\nA\niΔ\n\n\nS\niΔ\n\n\n\ni\n=\n1\n\n2\n…\nn\n\n\n obtained by sampling the price process and the attention factor at times \n\n\nt\ni\n\n=\niΔ\n,\ni\n=\n1\n,\n2\n,\n…\nn\n\n with constant observation step Δ; denote the logarithmic changes of the process by \n\n\nR\ni\n\n=\nlog\n\n\nS\niΔ\n\n\nS\n\n\n\ni\n−\n1\n\n\nΔ\n\n\n\n,\n\nP\ni\n\n=\nlog\n\n\nA\niΔ\n\n\nA\n\n\n\ni\n−\n1\n\n\nΔ\n\n\n\n\n and define \n\n\nX\ni\n\n≔\n\n∫\n\n\n\ni\n−\n1\n\n\nΔ\n\niΔ\n\n\nA\nu\n\ndu\n\n. Note that \n\n\nR\ni\n\n,\ni\n=\n1\n,\n2\n,\n…\nn\n\n represent the logarithmic returns of asset S for the sampling dates and that \n\n\nX\ni\n\n,\ni\n=\n1\n,\n2\n,\n…\nn\n\n the cumulative attention in the time interval \n\n[\n\n\ni\n−\n1\n\n\nΔ\n,\niΔ\n]\n\n. Then it is straightforward to prove the following:
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Theorem 2.1. The random vector\n\nR\n=\n\n\nR\n1\n\n\nR\n2\n\n\n…\n\nR\nn\n\n\n\n\n, given\n\nX\n=\n\n\nX\n1\n\n\nX\n2\n\n\n…\n\nX\nn\n\n\n\n\n, is normally distributed with mean\n\nm\n\nand covariance matrix\n\nΣ\n\nwhere
Proof. In order to prove the theorem it suffices to remind that, for i = 1, 2, …, n, the random variable \n\n\n∫\n\n\n\ni\n−\n1\n\n\nΔ\n\niΔ\n\n\n\nA\nu\n\n\n\ndW\nu\n\n\n, conditional on knowing \n\n\nX\ni\n\n\n, is normally distributed with zero mean and variance \n\n\nX\ni\n\n\n, and that the increments of the Brownian motion \n\nW\n\n are independent.
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As for the unconditional distribution, it is easy to obtain, for \n\ni\n=\n1\n,\n2\n,\n…\n,\nn\n\n,
where \n\nE\n\n\nX\ni\n\n\n,\nVar\n\n\nX\ni\n\n\n\n can be computed in closed form as a function of \n\n\nμ\nA\n\n,\n\nσ\nA\n\n,\nΔ\n\n (see for example [10]). The above outcomes are applied in order to derive the likelihood of the vector \n\n\nR\nX\n\n\n. Indeed, by simply applying Bayes’ rule, we get the following result:
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Proposition 2.2. The joint probability density of the vector \n\n\nR\nX\n\n\n is given by \n\ng\n:\nR\n×\n\nR\n+\n\n→\nR\n\n with
where \n\n\nf\n\nX\n1\n\n\n\n⋅\n\n\n and \n\n\nf\n\n\nX\ni\n\n∣\n\nX\n\ni\n−\n1\n\n\n\n\n\n⋅\n\n\n are the probability density function of \n\n\nX\n1\n\n\n and \n\n\nX\ni\n\n\n given \n\n\nX\n\ni\n−\n1\n\n\n\n, respectively.
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The proof follows from Bayes’ rule and application of Theorem 2.1.
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It is worth to remark that the probability density \n\ng\n\n⋅\n\n\n in Eq. (5) depends on suitable choices for \n\n\nf\n\nX\n1\n\n\n\n⋅\n\n\n and \n\n\nf\n\n\nX\ni\n\n∣\n\nX\n\ni\n−\n1\n\n\n\n\n\n⋅\n\n\n. Under our assumptions, such densities are not given within known distribution; however, by applying outcomes in [13], we can approximate them as log-normals with means and variances given as closed expressions of \n\n\n\nμ\nA\n\n\nσ\nA\n\n\n\n.
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Precisely, we have that \n\n\nf\n\nX\n1\n\n\n\n⋅\n\n=\nLN\n\nα\nν\n\n\n and, for \n\ni\n=\n2\n,\n3\n,\n…\nn\n,\n\nf\n\n\nX\ni\n\n∣\n\nX\n\ni\n−\n1\n\n\n\n\n\n⋅\n\n=\nLN\n\n\nα\ni\n\n\nν\ni\n\n\n\n, with
We apply the outcomes above in order to estimate model parameters according to the maximum-likelihood method (see for example [14, 15]) where the likelihood is approximated by applying the Levy approximation [13].
The first step in our procedure is to identify possible measures of investors’ attention. As already mentioned in the introduction, we consider the total trading volume on Bitcoin available from https://blockchain.info as well as the search volume index (SVI) for Google searches on the topic “bitcoin” provided by https://trends.google.it/trends/.
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The trading volume of exchange is a classical measure of the attractiveness of a traded asset for an investor; besides, in [16], the authors find evidence that the latter captures the attention of retail/uniformed investors.
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We consider daily data from January 1, 2015, to June 30, 2017, for the total volume and the SVI Index. As for the daily value of the Bitcoin, we have considered the average mean across main exchanges represented by the Index in https://blockchain.info.
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In Table 1, the outcomes for parameter estimates, obtained by maximizing the approximate likelihood given the observed time series, are summed up.
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\n
\n
\n
\n
\n
\n\n
\n
\n
\n\n\n\n\nμ\n̂\n\nA\n\n\n\n
\n
\n\n\n\n\nσ\n̂\n\nA\n\n\n\n
\n
\n\n\n\n\nμ\n̂\n\nS\n\n\n\n
\n
\n\n\n\n\nσ\n̂\n\nS\n\n\n\n
\n
\n\n\n
\n
A = Vol
\n
0.9571
\n
1.1346
\n
0.0218
\n
0.0829
\n
\n
\n
A = SVI
\n
1.3584
\n
1.0687
\n
0.0743
\n
0.1559
\n
\n\n
Table 1.
Parameter estimates for the model in Eq. (1) fitted on daily observations from January 2015 to June 2017.
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4. A closed formula for Bitcoin option prices
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In this section, we show how to characterize the price of European call options on Bitcoins in the underlying market model. Let us fix a finite time horizon \n\nT\n>\n0\n\n and assume the existence of a riskless asset (also called the savings account), whose price process \n\nB\n=\n\n\nB\nt\n\n\nt\n∈\n\n0\nT\n\n\n\n\n is given by
where \n\nr\n:\n\n0\nT\n\n→\nR\n\n is a bounded, deterministic function representing the instantaneous risk-free interest rate. To be reasonable, the market model must avoid arbitrage opportunities, that is, investment strategies that do not require an initial investment and that do not expose to any risk and lead to a positive value with positive probability. From a mathematical point of view, this means to check that the set of equivalent martingale measures for the Bitcoin price process \n\nS\n\n is nonempty. Precisely, it is possible to prove that it contains more than a single element.
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Lemma 3.1.Every equivalent martingale measure\n\nQ\n\nfor\n\nS\n\nis characterized by its density process with respect to the initial probability measure\n\nP\n\nas follows:
where\n\nγ\n=\n\n\nγ\nt\n\n\nt\n∈\n\n0\nT\n\n\n\n\nis an\n\nF\n\n-adapted process such that\n\n\n∫\n0\nT\n\n\n\nγ\nu\n\n2\n\ndu\n<\n+\n∞\n\n, \n\nP\n\n-a.s.
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The proof can be deduced from that of Lemma 1.4 in [10], where they also account for a possible delay between the attention factor and its effect on Bitcoin prices trend. The process \n\nγ\n\n can be interpreted as the risk perception associated to the future direction or future possible movements of the Bitcoin market. Since \n\nS\n\n is the only tradable asset, the risk perception is not fixed and this explains the nonuniqueness of the martingale measure \n\nQ\n\n in this market framework that turns out to be incomplete. Consequently, given any European-type contingent claim, it is not possible in general to find a self-financing strategy whose terminal value exactly replicates the payoff of the claim. We recall that the notion of completeness is related to the uniqueness of the martingale measure. Indeed, in complete markets, the no-arbitrage price of any derivative is uniquely determined by the unique martingale measure. On the other hand, in incomplete markets, we deal with a family of martingale measures and have at our disposal a set of possible prices, which are all compatible with the “no-arbitrage condition.” One common approach to option pricing in incomplete markets in the mathematical financial literature is to select one specific martingale measure (which can be also called pricing measure) under which the discounted traded assets are martingales and to compute option prices via expectation under this measure via risk-neutral evaluation formulas. One simple example of a candidate equivalent martingale measure is the so-called minimal martingale measure (see [17, 18]), which minimizes the relative entropy, of the objective measure \n\nP\n\n, with respect to any risk-neutral measure. In this setting, its economic interpretation is that agents do not wish to be compensated for the risk associated with the fluctuations of the stochastic attention factor, which corresponds to the hypothesis of [19] in the stochastic volatility framework. This is the probability measure which corresponds to the choice \n\nγ\n≡\n0\n\n in Eq. (10). Intuitively, under the minimal martingale measure, say \n\n\nP\n̂\n\n\n, the drift of the Brownian motion driving the Bitcoin price process is modified to make \n\nS\n\n an \n\nF\n\n-martingale, while the drift of the Brownian motion which is strongly orthogonal to \n\nS\n\n is not affected by the change measure from \n\nP\n\n to \n\n\nP\n̂\n\n\n. More precisely, by Girsanov’s theorem, the \n\n\nR\n2\n\n\n-valued process \n\n\n\nW\n̂\n\n\nZ\n̂\n\n\n=\n\n\n\n\nW\n̂\n\nt\n\n\n\nZ\n̂\n\nt\n\n\n\nt\n∈\n\n0\nT\n\n\n\n\n defined by
is an \n\n\nF\n\nP\n̂\n\n\n\n-standard Brownian motion. Under any equivalent martingale measure, the discounted Bitcoin price process \n\n\nS\n˜\n\n=\n\n\n\nS\n˜\n\nt\n\n\nt\n∈\n\n0\nT\n\n\n\n\n given by \n\n\n\nS\n˜\n\nt\n\n≔\n\n\nS\nt\n\n\nB\nt\n\n\n,\n\n for each \n\nt\n∈\n\n0\nT\n\n\n behaves like a martingale. Precisely, on the probability space \n\n\nΩ\nF\n\nP\n̂\n\n\n\n, the pair \n\n\n\nS\n˜\n\nA\n\n\n has the following dynamics:
where \n\nr\n\nt\n\n\n is the risk-free interest rate at time \n\nt\n\n.
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Remark 3.2.Note that, under any equivalent martingale measure that keeps the drift of the attention factor dynamics linear in\n\nA\n\n(in particular, under the minimal martingale measure), the model proposed in [10] nests the Hull-White stochastic volatility model, which corresponds to the particular case where\n\n\nσ\nS\n\n=\n1\n\n; see [19]. Indeed, the authors only referred to a risk-neutral framework without describing the dynamics under the physical measure and consequently characterizing the existence of any equivalent martingale measure.
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Now, we compute the fair price of a Bitcoin European call option via the risk-neutral evaluation approach, so it can be expressed as expected value of the terminal payoff under the selected pricing measure, that is, the minimal martingale measure. Let CT = (ST − K)+ be the \n\n\nF\nT\n\n\n-measurable random variable representing the payoff of a European call option on the Bitcoin with price \n\nS\n\n with date of maturity \n\nT\n\n and strike price \n\nK\n\n, which can be traded on the underlying digital market. Recall that \n\n\nX\n\nt\n,\nT\n\n\n=\n\nX\nT\n\n−\n\nX\nt\n\n\n, for each \n\nt\n∈\n\n0\nT\n\n\n, refers to the variation of the integrated attention process \n\nX\n\n defined over the interval \n\n\nt\nT\n\n\n. Then, denote by \n\n\nE\n\nP\n̂\n\n\n\n⋅\n\nF\nt\n\n\n\n the conditional expectation with respect to the \n\nσ\n\n-field \n\n\nF\nt\n\n\n under the probability measure \n\n\nP\n̂\n\n\n and so on. Define the function \n\n\nC\nBS\n\n:\n\n0\nT\n\n×\n\nR\n+\n\n×\n\nR\n+\n\n→\nR\n\n as follows:
The following result provides the risk-neutral price of the option under the minimal martingale measure \n\n\nP\n̂\n\n\n. The proof is straightforward and may be derived by using similar arguments to those developed in [19].
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Proposition 3.3. The risk-neutral price\n\n\nC\nt\n\n\nat time\n\nt\n\nof a European call option written on the Bitcoin with price\n\nS\n\nexpiring in\n\nT\n\nand with strike price\n\nK\n\nis given by the formula
where the function\n\n\nC\nBS\n\n\nis defined inEq. (15); the functions\n\n\nd\n1\n\n\n⋅\n\n\n, \n\n\nd\n2\n\n\n⋅\n\n\nare, respectively, given inEqs. (16)-(17); and\n\n\nf\n\nX\n\nt\n,\nT\n\n\n\n\n⋅\n\n\ndenotes the density function of\n\n\nX\n\nt\n,\nT\n\n\n\n, for each\n\nt\n∈\n\n0\nT\n\n\n, provided that it exists.
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Hence, the resulting risk-neutral pricing formula when evaluated in \n\n\nS\nt\n\n\n corresponds to the expected value of Black & Scholes price as defined in [20] at time \n\nt\n∈\n\n0\nT\n\n\n of a European call option written on \n\nS\n\n, with strike price \n\nK\n\n and maturity \n\nT\n\n, in a financial market where the volatility is random and given by \n\n\nσ\nS\n\n\n\n\nX\n\nt\n,\nT\n\n\n\nT\n−\nt\n\n\n\n\n.
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4.1. A numerical application
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In order to appreciate the performance of the pricing formula in Eq. (19), we compute model prices for option traded on the online platform http://www.deribit.com on July, 30, 2017, by plugging in the estimated parameters. The outcomes are compared with the Black & Scholes benchmark (see [20]) as a reference price, computed by plugging the volatility parameter estimated on the same time series of the trading volume/SVI index, and with the bid-ask prices provided in the website. Best overall pricing values are obtained when market attention is measured by volume; in the case of the SVI Google index, near-term options are very close to the mid-value of the bid-ask, while next-term options are overpriced. One possible explanation is that investors that get information about Bitcoin on search engines are more likely to be uninformed/retail investors that are self-exciting and may add spurious noise to the Bitcoin price volatility leading to an increase in call option prices (Table 2).
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\n
\n
\n
\n
\n
\n\n
\n
T-K
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Market bid
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Market ask
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Model volume
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Model Google SVI
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Benchmark BS
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\n\n\n
\n
Aug-2200
\n
0.1662
\n
0.2318
\n
0.2029
\n
0.2282
\n
0.1967
\n
\n
\n
Aug-2300
\n
0.1670
\n
0.2072
\n
0.1737
\n
0.2032
\n
0.1655
\n
\n
\n
Aug-2400
\n
0.1390
\n
0.1845
\n
0.1469
\n
0.1802
\n
0.1369
\n
\n
\n
Aug-2500
\n
0.1142
\n
0.1638
\n
0.1228
\n
0.1591
\n
0.1112
\n
\n
\n
Aug-2600
\n
0.0922
\n
0.1376
\n
0.1014
\n
0.1399
\n
0.0887
\n
\n
\n
Aug-2700
\n
0.0749
\n
0.1202
\n
0.0828
\n
0.1226
\n
0.0695
\n
\n
\n
Aug-2800
\n
0.0572
\n
0.1047
\n
0.0684
\n
0.107
\n
0.0535
\n
\n
\n
Aug-2900
\n
0.0442
\n
0.0983
\n
0.0549
\n
0.0931
\n
0.0405
\n
\n
\n
Sept-2200
\n
0.1991
\n
0.2648
\n
0.2546
\n
0.3204
\n
0.2173
\n
\n
\n
Sept-2300
\n
0.1766
\n
0.2432
\n
0.2321
\n
0.3019
\n
0.1906
\n
\n
\n
Sept-2400
\n
0.1890
\n
0.2230
\n
0.2113
\n
0.2844
\n
0.1662
\n
\n
\n
Sept-2500
\n
0.1375
\n
0.2042
\n
0.1919
\n
0.2679
\n
0.1439
\n
\n
\n
Sept-2600
\n
0.1207
\n
0.1828
\n
0.1741
\n
0.2523
\n
0.1239
\n
\n
\n
Sept-2700
\n
0.1120
\n
0.1668
\n
0.1576
\n
0.2377
\n
0.1060
\n
\n
\n
Sept-2800
\n
0.0953
\n
0.1504
\n
0.1463
\n
0.2239
\n
0.0903
\n
\n
\n
Sept-2900
\n
0.0848
\n
0.1422
\n
0.1325
\n
0.2109
\n
0.0764
\n
\n\n
Table 2.
Comparison between model prices computed according to formula in Eq. (19), Black & Scholes formula in [20], and the bid and ask prices provided in http:\\\\www.deribit.comfor options traded on July, 30, 2017, and expiring on August 25, 2017, and on September 28, 2017.
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5. The presence of model stock bubbles
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Motivated by empirical evidences (see for example [21, 22]), we discuss a generalization of the model introduced in Section 3.1, which is capable to describe speculative bubbles in Bitcoin markets.
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Precisely, we fix a finite time horizon \n\nT\n>\n0\n\n and assume that the underlying Brownian motions \n\nW\n\n and \n\nZ\n\n are correlated with constant correlation coefficient \n\nρ\n∈\n\n\n−\n1\n\n1\n\n\n, that is, \n\n<\nW\n,\nZ\n\n>\nt\n\n=\nρt\n\n for each \n\nt\n∈\n\n0\nT\n\n\n. If \n\nV\n=\n\n\nV\nt\n\n\nt\n∈\n\n0\nT\n\n\n\n\n is an additional \n\n\nF\nP\n\n\n-Brownian motion that is \n\nP\n\n-independent of \n\nZ\n\n, then we can write
Without loss of generality, we assume that the interest rate is fixed and equal to zero. In this setting, the discounted Bitcoin price trend and the market attention factor dynamics are described by
where we have set \n\n\nρ\n¯\n\n≔\n\n\n1\n−\n\nρ\n2\n\n\n\n\n. The aim is to investigate the existence of asset-price bubbles in the underlying Bitcoin market model.
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By simulating trajectories for the asset price \n\nS\n\n according to the model in Eq. (1) for several values of the correlation parameter, it seems that the latter is related to the presence of bubble effect; in fact, in Figure 2, we plot examples of trajectories for \n\nρ\n=\n0\n,\n−\n0.5\n,\n0.5\n,\n1\n\n, respectively where higher positive values for the correlation appear to boost the asset value.
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Figure 2.
Simulated trajectories with n = 250 daily observations for the attention process (red) and the corresponding Bitcoin price dynamics for \n\nρ\n=\n0\n\n (black), \n\nρ\n=\n0.5\n\n(green), and \n\nρ\n=\n1\n\n (blue).
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Indeed, we will show formally that the possibility of Bitcoin speculative bubbles is related to the sign of the correlation parameter \n\nρ\n\n.
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The mathematical theory of financial bubbles is developed, among others, in [23, 24, 25]. Precisely, we introduce the following definition from [23].
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Definition 4.1.The Bitcoin price process\n\nS\n\nhas a bubble on the time interval\n\n\n0\nT\n\n\nif\n\nS\n\nis a strict\n\nF\n\n-local martingale under the chosen risk-neutral measure.
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The term strict \n\nF\n\n-local martingale refers to the fact that \n\nS\n\n is an \n\nF\n\n-local martingale, but not a true \n\nF\n\n-martingale under the chosen risk-neutral measure. Further, since \n\nS\n\n is nonnegative, we must have that \n\nS\n\n is an \n\nF\n\n-supermartingale (we refer to [26] for rigorous definitions and related concepts).
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Recall that the absence of arbitrage opportunities is “essentially” equivalent to the existence of a probability measure \n\nQ\n\n, equivalent to the initial probability \n\nP\n\n, under which the discounted price process satisfies the martingale property.
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Remark 4.2.Note that stock bubbles arise if\n\nS\n\nhas an equivalent local martingale measure but not an equivalent martingale measure. Arbitrage appears only if no equivalent local martingale measure exists.
\n
Then, to exclude arbitrage opportunities from the market, we define the process \n\nL\n=\n\n\nL\nt\n\n\nt\n∈\n\n0\nT\n\n\n\n\n by setting
where \n\nλ\n=\n\n\nλ\nt\n\n\n\nt\n∈\n\n0\nT\n\n\n\n\n and \n\nγ\n=\n\n\nγ\nt\n\n\n\nt\n∈\n\n0\nT\n\n\n\n\n are \n\nF\n\n-adapted processes satisfying the integrability conditions \n\n\n∫\n0\nT\n\n\nλ\nu\n2\n\ndu\n<\n∞\n\n\n\nP\n\n-a.s. and \n\n\n∫\n0\nT\n\n\nγ\nu\n2\n\ndu\n<\n∞\n\n\n\nP\n\n-a.s., respectively. The (local) martingale property of the discounted Bitcoin price process \n\nS\n\n under \n\nQ\n\n implies the following condition:
To ensure that \n\nL\n\n provides the density process of a probability measure equivalent to \n\nP\n\n, we require that \n\nE\n\n\nL\nT\n\n\n=\n1\n\n, meaning that \n\nL\n\n is an \n\n\nF\nP\n\n\n-martingale. The processes \n\nλ\n\n and \n\nγ\n\n are interpreted, respectively, as the risk premium and the risk perception associated to the future direction or future possible movements of the Bitcoin market. For each choice of the process \n\nγ\n\n, the process \n\nλ\n\n is fixed by Eq. (23), that is,
and we can consider the corresponding family of equivalent (local) martingale measures \n\n\nQ\nγ\n\n\n for \n\nS\n\n parameterized by the process \n\nγ\n\n. To check if there are stock bubbles in the underlying market model, we study under which conditions the discounted Bitcoin price is a strict \n\n\nF\nP\n\n\n-local martingale with respect to an equivalent local martingale measure \n\n\nQ\nγ\n\n.\n\n By applying Girsanov’s theorem, the dynamics of the model under \n\n\nQ\nγ\n\n\n is described by the following equations:
where the \n\n\nR\n2\n\n\n-valued process \n\n\n\nV\n˜\n\n\nZ\n˜\n\n\n=\n\n\n\n\nV\n˜\n\nt\n\n\n\nZ\n˜\n\nt\n\n\n\nt\n∈\n\n0\nT\n\n\n\n\n defined by \n\n\n\nV\n˜\n\nt\n\n≔\n\nV\nt\n\n+\n\n∫\n0\nt\n\n\nλ\nu\n\ndu\n,\n\n.
\n
\n\n\n\n\nZ\n˜\n\nt\n\n≔\n\nZ\nt\n\n+\n\n∫\n0\nt\n\n\nγ\nu\n\ndu\n,\n\n is an \n\n\nF\n\nQ\nγ\n\n\n\n-standard Brownian motion.
\n
Now, suppose that the risk perception process is zero, that is, \n\nγ\n≡\n0\n\n. Then, the change of measure from \n\nP\n\n to \n\n\nQ\n0\n\n\n is well-defined since the associated density process \n\nM\n=\n\n\nM\nt\n\n\nt\n∈\n\n0\nT\n\n\n\n\n satisfying
is a true \n\n\nF\nP\n\n\n-martingale thanks to [27]. We have the following result, which allows to detect the presence of bubbles in this setting.
\n
Proposition 4.3.In the model outlined inEq. (24), the Bitcoin price process\n\nS\n\nhas a bubble on\n\n\n0\nT\n\n\nif and only if\n\nρ\n>\n0\n\n.
\n
The proof is based on the application of some of Sin’s results given in [27], where the existence of risk-neutral measures for the Hull-White stochastic volatility model [19] and for similar frameworks is determined by the possibility of explosion in finite time for solutions of certain auxiliary stochastic differential equations. Precisely, it is possible to show that the martingale property of the discounted stock price \n\nS\n\n under \n\n\nQ\n0\n\n\n, given in Eq. (25) with \n\nγ\n=\n0\n\n, is fulfilled if and only if \n\nρ\n≤\n0\n.\n\n Hence, a bubble arises if and only if the correlation parameter between stock returns and market attention is positive.
\n
\n
\n
6. Toward a multiexchange generalization
\n
Let us generalize the model introduced in Eq. (1) by assuming a possible delay \n\nτ\n\n for the attention factor to affect the Bitcoin price dynamics. Assume that the attention factor has been observed or is described by a deterministic function for \n\nt\n∈\n\n\n−\nl\n\n0\n\n\n with \n\nl\n≥\nτ\n\n. We get
Analogous results as those in Section 2 can be derived by similar computations, and model parameters, for a fixed delay, can be estimated by means of the maximum likelihood method. In order to estimate the delay parameter, we maximize the profile likelihood as defined in [15]. Details of this procedure can be found in [10]. The estimation results of model in Eq. (27) on the same daily data considered in Section 2 are summed up in Table 3.
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
\n
\n\n\nτ\n\n\n
\n
\n\n\n\n\nμ\n̂\n\nA\n\n\n\n
\n
\n\n\n\n\nσ\n̂\n\nA\n\n\n\n
\n
\n\n\n\n\nμ\n̂\n\nS\n\n\n\n
\n
\n\n\n\n\nσ\n̂\n\nS\n\n\n\n
\n
\n\n\n
\n
A = Vol
\n
1 day
\n
0.4881
\n
1.0459
\n
0.0282
\n
0.0924
\n
\n
\n
A = SVI
\n
7 days
\n
1.0964
\n
0.9946
\n
0.1005
\n
0.1885
\n
\n\n
Table 3.
Parameter estimates for model in Eq. (27) fitted on daily observations from January 2015 to June 2017.
\n
In Figure 3, we plot simulated trajectories of the price process in Eq. (27) by letting the delay parameter vary.
\n
Figure 3.
Simulated trajectories of n = 250 daily observations of the attention factor (red) and the Bitcoin price according to model in Eq. (27) when the delay parameter is \n\nτ\n=\n1\n\n day (black) and \n\nτ\n=\n10\n\n days (blue).
\n
The different delays result in a shift to the south-east between the faster and slower reacting trajectories; in the picture, this behavior is sharp since the other model parameters are kept constant. By looking at the picture, the idea to model the price of Bitcoin in different exchanges by the same model in Eq. (27) but allowing different parameters naturally arises.
\n
In particular, considering for instance two exchanges, we have
where \n\nφ\n:\n\n\n−\nl\n\n0\n\n→\n\nR\n+\n\n\n with \n\nl\n>\nmax\n\n\nτ\n1\n\n\nτ\n2\n\n\n\n and \n\n\nμ\nA\ni\n\n,\n\nμ\nS\ni\n\n,\n\nσ\nA\ni\n\n>\n0\n,\n\nσ\nS\ni\n\n>\n0\n\n for i = 1, 2 are constant parameters.
\n
Note that within this model, prices for Bitcoin traded in different exchanges are perfectly correlated. Indeed, this is what happens in observed data; considering daily prices from January 2015 to June 2017 for Bitstamp, Kraken, Cex.io, Gdax, and The Rock exchanges we get cross-correlation values larger than 0.999.
\n
We fit model in Eq. (28) for the Bitstamp and Gdax exchanges on daily observations of Bitcoin price from January 2015 to June 2017 obtaining the outcomes reported in Table 4, when the attention is measured by the trading volume, and in Table 5, when attention is measured by the Google SVI index.
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
Exchange
\n
\n\n\nτ\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\n
\n
\n\n\n\nσ\nA\n\n\n\n
\n
\n\n\n\nμ\nS\n\n\n\n
\n
\n\n\n\nσ\nS\n\n\n\n
\n
\n\n\n
\n
Bitstamp
\n
1
\n
0.4994
\n
1.0461
\n
0.0281
\n
0.0896
\n
\n
\n
Gdax
\n
2
\n
0.4997
\n
1.0420
\n
0.0326
\n
0.1036
\n
\n\n
Table 4.
Model fitting with delay parameter: outcomes for Bitstamp and Gdax exchanges when attention is measured by the trading volume.
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
Exchange
\n
\n\n\nτ\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\n
\n
\n\n\n\nσ\nA\n\n\n\n
\n
\n\n\n\nμ\nS\n\n\n\n
\n
\n\n\n\nσ\nS\n\n\n\n
\n
\n\n\n
\n
Bitstamp
\n
7 days
\n
1.0934
\n
0.9946
\n
0.0992
\n
0.1782
\n
\n
\n
Gdax
\n
7 days
\n
1.0964
\n
0.9946
\n
0.1160
\n
0.2087
\n
\n\n
Table 5.
Model fitting with delay parameter: outcomes for Bitstamp and Gdax exchanges when attention is measured by the SVI index.
\n
It is evident from the outcomes in Table 4 that the model parameters are not significantly different while the delay might be quite different as if the reaction to the attention factor is faster for some exchanges and slower for others. On the contrary, when attention is measured by the Google SVI Index, the delay is unchanged, but the difference between estimated parameters for the price dynamics is nonnegligible.
\n
By analyzing the outcomes and considering the shift effect as depicted in Figure 3, it is tempting to conjecture that the faster reaction determines the leader exchanges and that the slower exchange will then follow. If we could forecast that the next day price of the slower exchange will reach the price today for the faster one, we could obtain a profit by suitably investing in the two exchanges. However, it is worth noticing that the estimation of the delay parameter is obtained by maximizing the likelihood over a whole time series and is a product of averaging so arbitrage cannot be achieved in a direct way.
\n
Nevertheless, in a multivariate setting as ours, the theory guarantees that arbitrage opportunities are ruled out if the market price of risk in the market is unique. Without entering technical details and assuming \n\nr\n=\n0\n\n for the sake of simplicity, this is true if and only if
It is evident that these values are not equal if we plug parameter estimates in Eq. (30); hence, arbitrage opportunities are not ruled out at least from a theoretical point of view. We will address this issue more precisely in future research.
\n
\n
\n
7. Conclusion
\n
In this chapter, we have introduced a model in continuous time in order to describe the dynamics of Bitcoin price depending on an exogenous stochastic factor, which represents market attention on the Bitcoin system. Market attention is measured either by the total trading volume in Bitcoins or by means of the Google Search Volume Index, which, as suggested in [16], is a direct measure of the revealed attention for uniformed retail investors. More precisely, the attention factor affects directly the instantaneous mean and volatility of logarithmic returns; in addition, it may be also correlated with the price changes. An estimation procedure to fit the model to observed data is also suggested and, under the assumption of no correlation, a closed formula for standard European option prices on Bitcoin is provided.
\n
By applying outcomes within the mathematical theory of bubbles [23, 24, 25, 27], we are able to show that Bitcoin boosts in a bubble if and only if there is a positive correlation between changes in the price and in the attention factor. This finding is reasonable and claims that a stronger positive dependence between the two processes in Eq. (21) may result in an explosion of the price process.
\n
Finally, we allow for a delay on the effect of market attention on the Bitcoin price, and, based on this generalized model, we introduce a multivariate setting for our model (Eq. (28)) in order to take into account the special feature of multiple exchanges where it is possible to trade in Bitcoins. Preliminary results indicate that arbitrage opportunities may arise in two exchanges that are characterized by different delays.
\n
\n
Acknowledgments
\n
We gratefully acknowledge Marco Patacca for having provided the routines in Matlab® to develop the empirical sections of the paper and for useful suggestions and comments. We also acknowledge funding from Fondazione Cassa di Risparmio di Perugia (Grant 2015:0459013) and Bank of Italy (Grant 407660/16).
\n
Conflict of interest
The authors declare no conflict of interest.
\n
Thanks
\n
Gianna Figà-Talamanca gratefully acknowledges interesting discussions on the topic of this chapter with colleagues of the Department of Finance and Risk Engineering where she was visiting professor while preparing this research. The authors also wish to thank Stefano Bistarelli for having introduced them to the intriguing and worth to explore world of cryptocurrencies.
\n
\n',keywords:"Bitcoin, market attention, arbitrage, option pricing, bubbles",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/62627.pdf",chapterXML:"https://mts.intechopen.com/source/xml/62627.xml",downloadPdfUrl:"/chapter/pdf-download/62627",previewPdfUrl:"/chapter/pdf-preview/62627",totalDownloads:1041,totalViews:0,totalCrossrefCites:1,dateSubmitted:"February 15th 2018",dateReviewed:"June 8th 2018",datePrePublished:"November 5th 2018",datePublished:"August 28th 2019",dateFinished:null,readingETA:"0",abstract:"The goal of this chapter is to present recent developments about Bitcoin1 price modeling and related applications. Precisely, we consider a bivariate model in continuous time to describe the behavior of Bitcoin price and of the investors’ attention on the overall network. The attention index affects Bitcoin price through a suitable dependence on the drift and diffusion coefficients and a possible correlation between the sources of randomness represented by the driving Brownian motions. The model is fitted on historical data of Bitcoin prices, by considering the total trading volume and the Google Search Volume Index as proxies for the attention measure. Moreover, a closed formula is computed for European-style derivatives on Bitcoin. Finally, we discuss two possible extensions of the model. Precisely, we investigate the relation between the correlation parameter and possible bubble effects in the asset price; further, we consider a multivariate framework to represent the special feature of Bitcoin being traded on several exchanges and we discuss conditions to rule out arbitrage opportunities in this setting.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/62627",risUrl:"/chapter/ris/62627",signatures:"Alessandra Cretarola and Gianna Figà-Talamanca",book:{id:"7228",title:"Blockchain and Cryptocurrencies",subtitle:null,fullTitle:"Blockchain and Cryptocurrencies",slug:"blockchain-and-cryptocurrencies",publishedDate:"August 28th 2019",bookSignature:"Asma Salman and Muthanna G. Abdul Razzaq",coverURL:"https://cdn.intechopen.com/books/images_new/7228.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"206443",title:"Dr.",name:"Asma",middleName:null,surname:"Salman",slug:"asma-salman",fullName:"Asma Salman"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"246178",title:"Prof.",name:"Alessandra",middleName:null,surname:"Cretarola",fullName:"Alessandra Cretarola",slug:"alessandra-cretarola",email:"alessandra.cretarola@unipg.it",position:null,institution:null},{id:"246179",title:"Prof.",name:"Gianna",middleName:null,surname:"Figà-Talamanca",fullName:"Gianna Figà-Talamanca",slug:"gianna-figa-talamanca",email:"gianna.figatalamanca@unipg.it",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. The Bitcoin network",level:"1"},{id:"sec_3",title:"3. An attention-based model",level:"1"},{id:"sec_3_2",title:"3.1. The model specification",level:"2"},{id:"sec_4_2",title:"3.2. Statistical properties and model fitting",level:"2"},{id:"sec_5_2",title:"3.3. Empirical application on Bitcoin prices",level:"2"},{id:"sec_7",title:"4. A closed formula for Bitcoin option prices",level:"1"},{id:"sec_7_2",title:"4.1. A numerical application",level:"2"},{id:"sec_9",title:"5. The presence of model stock bubbles",level:"1"},{id:"sec_10",title:"6. Toward a multiexchange generalization",level:"1"},{id:"sec_11",title:"7. Conclusion",level:"1"},{id:"sec_12",title:"Acknowledgments",level:"1"},{id:"sec_15",title:"Conflict of interest",level:"1"},{id:"sec_12",title:"Thanks",level:"1"}],chapterReferences:[{id:"B1",body:'Nakamoto S. Bitcoin: A Peer-To-Peer Electronic Cash System. 2009. http://www.Bitcoin.org\n\n'},{id:"B2",body:'Urquhart A. The inefficiency of bitcoin. Economics Letters. 2016;148:80-82\n'},{id:"B3",body:'Dyhrberg AO. Bitcoin, gold and the dollar–A garch volatility analysis. Finance Research Letters. 2016;16:85-92\n'},{id:"B4",body:'Katsiampa P. Volatility estimation for bitcoin: A comparison of garch models. Economics Letters. 2017;158:3-6\n'},{id:"B5",body:'Kristoufek L. BitCoin meets Google trends and Wikipedia: Quantifying the relationship between phenomena of the internet era. Scientific Reports. 2013;3(3415):1-7\n'},{id:"B6",body:'Kristoufek L. What are the main drivers of the bitcoin price? Evidence from wavelet coherence analysis. PLoS One. 2015;10(4):e0123923\n'},{id:"B7",body:'Bukovina J, Marticek M. Sentiment and bitcoin volatility. Technical report, Mendel University in Brno, Faculty of Business and Economics; 2016\n'},{id:"B8",body:'Figà-Talamanca G, Patacca M. Does market attention affect Bitcoin returns and volatility? SSRN Electronic Journal. 2018:11\n'},{id:"B9",body:'Blau BM. Price dynamics and speculative trading in bitcoin. Research in International Business and Finance. 2017;41:493-499\n'},{id:"B10",body:'Cretarola A, Figà-Talamanca G, Patacca M. Market Attention and Bitcoin Price Modeling: Theory, Estimation and Option Pricing. Submitted; 2018\n'},{id:"B11",body:'Kim YB, Lee SH, Kang SJ, Choi MJ, Lee J, Kim CH. Virtual world currency value fluctuation prediction system based on user sentiment analysis. PLoS One. 2015;10(8):e0132944\n'},{id:"B12",body:'Yermack D. Is bitcoin a real currency? An economic appraisal. In: Handbook of Digital Currency. USA: Academic Press; 2015. pp. 31-43\n'},{id:"B13",body:'Levy E. Pricing European average rate currency options. Journal of International Money and Finance. 1992;11(5):474-491\n'},{id:"B14",body:'Davison AC. Statistical Models, Volume 11. USA: Cambridge University Press; 2003\n'},{id:"B15",body:'Pawitan Y. In all Likelihood: Statistical Modelling and Inference Using Likelihood. UK: Oxford University Press; 2001\n'},{id:"B16",body:'Da Z, Engelberg J, Gao P. In search of attention. The Journal of Finance. 2011;66(5):1461-1499\n'},{id:"B17",body:'Föllmer H, Schweizer M, Hedging of contingent claims under incomplete information. In M.H.A Davis and R.J.Elliot, editors, Applied Stochastic Analysis. New York, Gordon and Breach. 1991;5:389‐414\n'},{id:"B18",body:'Föllmer H, Schweizer M. Minimal martingale measure. In: Encyclopedia of Quantitative Finance. Wiley Online Library; 2010\n'},{id:"B19",body:'Hull J, White A. The pricing of options on assets with stochastic volatilities. The Journal of Finance. 1987;42(2):281-300\n'},{id:"B20",body:'Black F, Scholes M. The pricing of options and corporate liabilities. The Journal of Political Economy. 1973:81(3):637-654\n'},{id:"B21",body:'Malhotra A, Maloo M. Bitcoin–Is it a bubble? Evidence from unit root tests. SSRN Electronic Journal. 2014:13\n'},{id:"B22",body:'Corbet S, Lucey B, Yarovya L. Datestamping the Bitcoin and Ethereum bubbles. Finance Research Letters. 2017:8 (In press)\n'},{id:"B23",body:'Jarrow RA, Protter PE, Shimbo K. Asset price bubbles in incomplete markets. Mathematical Finance. 2010;20(2):145-185\n'},{id:"B24",body:'Protter PE. A mathematical theory of financial bubbles. In: Paris-Princeton Lectures on Mathematical Finance. Switzerland: Springer; 2013. pp. 1-108\n'},{id:"B25",body:'Protter PE. Bubbles and crashes - mathematical models of bubbles. Quantitative Finance Letters. 2016;4:10-13\n'},{id:"B26",body:'Protter PE. Stochastic Integration and Differential Equations. Germany: Springer; 2005\n'},{id:"B27",body:'Sin CA. Complications with stochastic volatility models. Advances in Applied Probability. 1998;30(1):256-268\n'}],footnotes:[{id:"fn1",explanation:"We use the following rule throughout the paper: the term BitCoin refers to the whole system network while Bitcoin refers to the digital currency."}],contributors:[{corresp:"yes",contributorFullName:"Alessandra Cretarola",address:"alessandra.cretarola@unipg.it",affiliation:'
Department of Mathematics and Computer Science, University of Perugia, Italy
Department of Economics, University of Perugia, Italy
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Semchyshyn graduated from the the Yuriy Fedkovych Chernivtsi State University, Ukraine in 1990 with MSc degree in Analytical \nChemistry. In 1993 she obtained Doctoral Scholarship at the Department of Biochemistry of Ivano-Frankivsk Medical State Academy (Ukraine). After defending her Ph.D. thesis in 2002, she started working as an Assistant Professor and and as an Associate Professor at the Department of Biochemistry and Biotechnology of Vassyl Stefanyk \nPrecarpathian University Ivano-Frankivsk, Ukraine. From 2006 to 2011 she worked as a visiting researcher and a visiting professor at the Jagiellonian University, Poland and at the Lund University, Sweden. Her current research is related to dual role of reactive oxygen and carbonyl species, interplay between different kinds of stresses, and organisms’ \nadaptations to environmental challenges.",institutionString:null,institution:{name:"Vasyl Stefanyk Precarpathian National University",institutionURL:null,country:{name:"Ukraine"}}},{id:"108752",title:"Dr.",name:"Padmini",surname:"Ghugre",slug:"padmini-ghugre",fullName:"Padmini Ghugre",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"128379",title:"Prof.",name:"Knox",surname:"Van Dyke",slug:"knox-van-dyke",fullName:"Knox Van Dyke",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null}]},generic:{page:{slug:"OA-publishing-fees",title:"Open Access Publishing Fees",intro:"
The Open Access model is applied to all of our publications and is designed to eliminate subscriptions and pay-per-view fees. This approach ensures free, immediate access to full text versions of your research.
As a gold Open Access publisher, an Open Access Publishing Fee is payable on acceptance following peer review of the manuscript. In return, we provide high quality publishing services and exclusive benefits for all contributors. IntechOpen is the trusted publishing partner of over 118,000 international scientists and researchers.
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1,400 GBP Chapter - Edited Volume
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4,000 GBP Compacts Monograph - Short Form
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*These prices do not include Value-Added Tax (VAT). Residents of European Union countries need to add VAT based on the specific rate in their country of residence. Institutions and companies registered as VAT taxable entities in their own EU member state will not pay VAT as long as provision of the VAT registration number is made during the application process. This is made possible by the EU reverse charge method.
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Services included are:
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English language copyediting and proofreading, including the correction of grammatical, spelling, and other common errors
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XML Typesetting and pagination - web (PDF, HTML) and print files preparation
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Discoverability - electronic citation and linking via DOI
\\n\\t
Permanent and unrestricted online access to your work
What isn't covered by the Open Access Publishing Fee?
\\n\\n
If your manuscript:
\\n\\n
\\n\\t
Exceeds 20 pages (for chapters in Edited Volumes), an additional fee of 40 GBP per page will be required
\\n\\t
If a manuscript requires Heavy Editing or Language Polishing, this will incur additional fees.
\\n
\\n\\n
Your Author Service Manager will inform you of any items not covered by the OAPF and provide exact information regarding those additional costs before proceeding.
\\n\\n
Open Access Funding
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To explore funding opportunities and learn more about how you can finance your IntechOpen publication, go to our Open Access Funding page. IntechOpen offers expert assistance to all of its Authors. We can support you in approaching funding bodies and institutions in relation to publishing fees by providing information about compliance with the Open Access policies of your funder or institution. We can also assist with communicating the benefits of Open Access in order to support and strengthen your funding request and provide personal guidance through your application process. You can contact us at oapf@intechopen.com for further details or assistance.
\\n\\n
For Authors who are still unable to obtain funding from their institutions or research funding bodies for individual projects, IntechOpen does offer the possibility of applying for a Waiver to offset some or all processing feed. Details regarding our Waiver Policy can be found here.
\\n\\n
Added Value of Publishing with IntechOpen
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Choosing to publish with IntechOpen ensures the following benefits:
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Indexing and listing across major repositories, see details ...
\\n\\t
Long-term archiving
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Visibility on the world's strongest OA platform
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Live Performance Metrics to track readership and the impact of your chapter
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Dissemination and Promotion
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Benefits of Publishing with IntechOpen
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Proven world leader in Open Access book publishing with over 10 years experience
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+4,800 OA books published
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Most competitive prices in the market
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Fully compliant with OA funding requirements
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Optimized processes, enabling publication between 8 and 12 months
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Personal support during every step of the publication process
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+146,150 citations in Web of Science databases
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Currently strongest OA platform with over 130 million downloads
As a gold Open Access publisher, an Open Access Publishing Fee is payable on acceptance following peer review of the manuscript. In return, we provide high quality publishing services and exclusive benefits for all contributors. IntechOpen is the trusted publishing partner of over 118,000 international scientists and researchers.
\n\n
The Open Access Publishing Fee (OAPF) is payable only after your full chapter, monograph or Compacts monograph is accepted for publication.
\n\n
OAPF Publishing Options
\n\n
\n\t
1,400 GBP Chapter - Edited Volume
\n\t
10,000 GBP Monograph - Long Form
\n\t
4,000 GBP Compacts Monograph - Short Form
\n
\n\n
*These prices do not include Value-Added Tax (VAT). Residents of European Union countries need to add VAT based on the specific rate in their country of residence. Institutions and companies registered as VAT taxable entities in their own EU member state will not pay VAT as long as provision of the VAT registration number is made during the application process. This is made possible by the EU reverse charge method.
\n\n
Services included are:
\n\n
\n\t
An online manuscript tracking system to facilitate your work
\n\t
Personal contact and support throughout the publishing process from your dedicated Author Service Manager
\n\t
Assurance that your manuscript meets the highest publishing standards
\n\t
English language copyediting and proofreading, including the correction of grammatical, spelling, and other common errors
\n\t
XML Typesetting and pagination - web (PDF, HTML) and print files preparation
\n\t
Discoverability - electronic citation and linking via DOI
\n\t
Permanent and unrestricted online access to your work
What isn't covered by the Open Access Publishing Fee?
\n\n
If your manuscript:
\n\n
\n\t
Exceeds 20 pages (for chapters in Edited Volumes), an additional fee of 40 GBP per page will be required
\n\t
If a manuscript requires Heavy Editing or Language Polishing, this will incur additional fees.
\n
\n\n
Your Author Service Manager will inform you of any items not covered by the OAPF and provide exact information regarding those additional costs before proceeding.
\n\n
Open Access Funding
\n\n
To explore funding opportunities and learn more about how you can finance your IntechOpen publication, go to our Open Access Funding page. IntechOpen offers expert assistance to all of its Authors. We can support you in approaching funding bodies and institutions in relation to publishing fees by providing information about compliance with the Open Access policies of your funder or institution. We can also assist with communicating the benefits of Open Access in order to support and strengthen your funding request and provide personal guidance through your application process. You can contact us at oapf@intechopen.com for further details or assistance.
\n\n
For Authors who are still unable to obtain funding from their institutions or research funding bodies for individual projects, IntechOpen does offer the possibility of applying for a Waiver to offset some or all processing feed. Details regarding our Waiver Policy can be found here.
\n\n
Added Value of Publishing with IntechOpen
\n\n
Choosing to publish with IntechOpen ensures the following benefits:
\n\n
\n\t
Indexing and listing across major repositories, see details ...
\n\t
Long-term archiving
\n\t
Visibility on the world's strongest OA platform
\n\t
Live Performance Metrics to track readership and the impact of your chapter
\n\t
Dissemination and Promotion
\n
\n\n
Benefits of Publishing with IntechOpen
\n\n
\n\t
Proven world leader in Open Access book publishing with over 10 years experience
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+4,800 OA books published
\n\t
Most competitive prices in the market
\n\t
Fully compliant with OA funding requirements
\n\t
Optimized processes, enabling publication between 8 and 12 months
\n\t
Personal support during every step of the publication process
\n\t
+146,150 citations in Web of Science databases
\n\t
Currently strongest OA platform with over 130 million downloads
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