Towards a transdisciplinary econophysics

Abstract

This paper deals with the disciplinary dimension of a very new field called econophysics and shows that despite the fact that econophysics is regularly described as an interdisciplinary approach, it is in fact a multidisciplinary field. Beyond this observation, we note that recent developments suggest that econophysics could evolve towards a more integrated field. We therefore propose a prospective approach by analyzing how this field could become transdisciplinary. In this article, we focus on financial work, and we show that a common scheme is attainable and we investigate the possibilities of a trandisciplinary econophysics which will make possible to revisit the theoretical foundations of financial economics and develop new models and theories better suited to the management of financial risks and financial markets.

Keywords:

• econophysics
• financial economics
• interdisciplinarity
• multidisciplinarity
• pluridisciplinarity
• transdisciplinarity

Notes

The contribution of this article is twofold: on the one hand it clarifies the epistemological status of econophysics, and on the other, it studies the recent evolution of econophysics and shows how this field could evolve to become transdisciplinary.

 1. On the history of econophysics, see Jovanovic and Schinckus (2013), Roehner (2002) or Daniel and Sornette (2010).

 2. The leptokurticity of financial distribution is a very old issue (Mitchell, for example, recognized the presence of kurtosis in financial return in 1915). Likewise in economics, a specific case of this statistical framework (Paretian law) had been used before Mandelbrot's work (for example, by Pareto, who pioneered the use of power law distributions even prior to their use in physics). However, Jovanovic and Schinckus (2013) explained why the application of models taken from statistical mechanics (stable Lévy processes) to financial economics was not used in finance before the 1960s. For further details about the use of power laws in economics and social sciences, see also Plerou et al. (2000).

 3. More specifically, Mandelbrot's stable Lévy processes and their fractality, thanks to the statistical stability of these processes, were used to characterize the phenomenon of turbulence. Mandelbrot showed that it was possible to find a complex regularity (fractality) through statistical stability. In this regard, stable Lévy processes produced a statistical interpretation of his fractal geometry (Mandelbrot 1999). See Mirowski (1990) for further details about the analogy of financial markets with fractal geometry.

 4. The basic incompatibility stems from the indeterminacy of variance in Lévy processes. From a financial perspective, this would imply indeterminacy of the measurement of risk. We evoke this point in the last part of this article.

 5. The first definition of econophysics given by Stanley was more sociological: he wrote that econophysics is ‘a multidisciplinary field… that denotes the activities of physicists who are working on economic problems to test a variety of new conceptual approaches from the physical sciences’ (Mantegna & Stanley, 2000, pp. viii–ix). However, this sociological definition generates an epistemological contradiction: if econophysics involves the activity of physicists only, it cannot be a multidisciplinary field, because that would require a minimum of collaboration between specialists from different disciplinary contexts, implying therefore that other theoreticians can also do econophysics. If physics can legitimately be considered as the purview of physicists, why should econophysics be seen as a ‘reserved area’ for physicists? The rest of this paper will explore such questions.

 6. Agent-based modelling is based on computerized simulations of a large number of decision makers that can interact through specified procedures. The agent-based approach appeared in the 1990s as a new tool for empirical research in a number of fields: economics (Axtell, 1999), voting behaviour (Lindgren & Nordahl, 1994), military tactics (Ilachinski, 2000), organizational behaviour (Prietula et al., 1998), epidemics (Epstein & Axtell, 1996), traffic congestion patterns (Nagel & Rasmussen, 1994), etc.

 7. One of the first authors to bring physics closer to the financial domain was Jules Regnault in the second half of the nineteenth century (Jovanovic, 2006; Jovanovic & Le Gall, 2001). In the twentieth century, a number of physics concepts played a part in the development of modern financial theory. The best known application of physics to finance is the application of the heat-diffusion formula (Bachelier, Black and Scholes) and a number of studies implicitly or explicitly referred to a concept from the field of physics: Brownian motion (Jovanovic, 2009).

 8. Of course, there are physicists doing economics and economists with advanced degrees in physics, but these theoreticians always try to give an economic meaning to their importation of concepts from physics. The specificity of econophysics lies in an absence of economic, meaning: econophysicists consider economic systems simply as physical systems, with no transfer of economic meaning to the final results.

 9. Some authors (Israel, 2005; McCauley, 2004) argue that the idea of ‘emergence’ is empty and should be replaced by the physics-based concept of invariance, Rosser (2008a) showed that the distinction between the two is irrelevant and results from the old methodological struggle between the continuous and the discrete. See Rosser (2008a) for a very good introduction to this point.

10. Some econophysicists (McCauley, for example) attribute an ontological nature to these regularities since they consider them a kind of ‘universality’ (see Rickles, 2007 for an analysis of universal law in econophysics).

11. These scaling laws can then be viewed as a macro result of the behaviour of a large number of interacting components from lower levels. As Rickles (2007, p. 7) explains, ‘The idea is that in statistical physics, systems that consist of a large number of interacting parts often are found to obey “universal laws” – laws independent causally of microscopic details and dependent on just a few macroscopic parameters’.

12. Even if power law distributions are also used to characterize many phenomena in social sciences, such as the ranking of firm size (Stanley et al., 1996); the income distribution of companies (Okuyama et al., 1999); fluctuations in finance (Mandelbrot, 1997), these laws are often replaced by log-normal laws in which the variance parameter is not infinite.

13. Pareto, in his Cours d'Economie Politique (1897), was the first to investigate the statistical character of the wealth of individuals by modelling them using power laws.

14. If α>2, then the Lévy process is no longer stable.

15. As Nicolesu (2010, p. 22) pointed out, ‘there is no opposition between disciplinarity (including inter-multi disciplinarity) and transdisciplinarity but there is instead a fertile complementarity, In fact, there is no transdisciplinarity without disciplinarity’.

16. See Jovanovic (2010) for an illustration with efficient market theory.

17. The adjective ‘indeterminate’ would be more accurately employed, but the literature uses ‘infinite’.

18. Of course, financial economists know that financial distributions are not empirically Gaussian. Therefore, they have developed a large variety of statistical processes to better understand the dynamics of financial markets. However, all these statistical solutions imply either a Gaussian world (with continuity where an optimal hedging is possible and therefore in line with the theoretical framework defined by Harrisson, Kreps and Pliska) or a non-Gaussian framework (discontinuous pump processes) in which a perfect riskless hedge is not plausible (and therefore in opposition to the dominant axiomatics defined by Harrisson, Kreps and Pliska). Work in the first category falls into what we call the ARCH types models, which remain implicitly based on a Gaussian framework since they consider that unconditional distributions are governed by Gaussian processes (whose tails can be fatter and then explained in terms of conditional distribution). In other words, these models provide a statistical description (which can be non-Gaussian) of the variance observed in unconditional distribution. As mentioned above, work in the second category involves jump processes, which are based on a discontinuous process describing the financial distribution – implying that a perfect hedging strategy is inconceivable. Moreover, the large number of statistical processes used in this specific literature does not favour the crystallization of a unified financial theory. [For further information about this distinction, see Rachev et al. (2011) or Schinckus (2012)].

19. Of course, there exist some measures of risk that are not based on variance (Fama & Roll, 1971; Markowitz, 1959). Moreover, it is worth mentioning that the association of risk with variance implies a specific dependence between random variables which is not invariant under non-linear, strictly increasing transformation. However, asset prices are a strictly increasing function of return, but the correlation structure is not maintained by this kind of transformation, meaning that returns could be uncorrelated whereas prices are strongly correlated and vice versa. Use of a specific function called copula is then in order to characterize this particular dependency between random variables. See Embrechts (2009) for further information.

20. With Rosser (2006, 2008b), Keen is one of the rare breed of economists who have engaged with econophysicists.

21. McCauley (2006, p. 17) did not hesitate to compare financial theory to cartoons: ‘the multitude of graphs presented without are not better than cartoons because they are not based on real empirical data only on falsified neoclassical expectations.’

22. A survey we conducted supports this interpretation: econophysicists' manuscripts are often rejected by economic journals because their empirical approach is different from that of economists.

23. See Gingras and Schinckus (2012) for a more sociological analysis of the emergence of econophysics.

24. Galison (1997) explained how engineers collaborated with physicists in order to develop particle detectors and radar.

25. The Creole language is often presented as an example of a pidgin because it results from a mix of regional languages (Chavacano from the Philippines, Krio from Sierra Leone and Tok from Papua New Guinea); see Todd (1990).

26. What philosophers of science call the ‘physical claim’ of models used in physics (Barberousse, Franceschelli, & Imbert, 2009). See also Schinckus (2013) for further information about how econophysicists made stable Lévy processes physically plausible.

27. Note that truncated stable Lévy processes can be seen as the statistical solution to the problem of infinite variance emphasized by Mandelbrot (1963) and Fama (1965).

28. Truncation is a specific calibration of statistical distribution which must not be confused with a linear transformation of distribution – for example, the use of log-normality.

29. It was Harrison and Kreps (1979), Harrison and Pliska (1981) and Kreps (1981) gave a rigorous mathematical framework to definitions, hypotheses and results that constitute the heart of modern financial theory.

30. Only non-truncated Lévy processes are stable (Mandelbrot, 1963).

31. This implies that its shape is changing at different time horizons and that distribution at different time horizons do not obey scaling relations. Indeed, the variable x progressively converges towards a Lévy distribution for x < N ^* while it converges towards to a normal distribution when x is beyond the crossover value N ^*. More precisely, scaling turns out to be approximate and valid for a finite time interval only. For longer time intervals, scaling must break down. Moreover, some physicists have claimed that an abrupt truncation is only useful for very specific cases, but that this methodology would not be sufficiently physically plausible.

32. Stable Lévy processes are a specific case of pure-jump processes and, as noted earlier, it is generally accepted that a pure-jump process corresponds to an incomplete market (Nolan, 2009). However, a stable Lévy framework is not a strictly compound jump-process. Carr and Wu (2003, p. 754) explained that in contrast to a standard Poisson or compound Poisson process, this pure jump process [stable Lévy process] has an infinite number of jumps over any time interval, allowing it to capture the extreme activity traditionally handled by diffusion processes. Most of the jumps are small and may be regarded as approximating the transition from one decimalized price to another one nearby. In this perspective, stable Lévy processes can be seen as quasi-continuous processes, as emphasized by Nolan (2009).

33. They approach the continuous limit, being composed of an infinite number of small jumps in each time interval. This feature would make it possible to link these processes with research into the uniqueness of option prices.

34. Even when financial economists use models derived from ARCH (EGARCH, GARCH, etc.) to capture the leptokurticity of financial distributions, they implicitly assume that these distributions are Gaussian. Moreover, although, the standard ARCH model used in finance can reproduce the power-law distribution of returns, they assume finite memory on past events and hence they are not consistent with long-range correlations in volatility observed on the market. It is worth mentioning that some authors have recommended the development of non-Gaussian alternatives, which would be based on complex heuristics, providing rules of thumb to practitioners (Haug & Taleb, 2011).

35. Financial economists usually use the concept of kurtosis to describe the leptokurticity of a distribution. However, this statistical concept is a Gaussian parameter (Balanda & MacGillivray, 1988) and it often underestimates the leptokurticity in comparison with observed results (Tankov, 2004).

36. The Hurst exponent is the scaling property of the fractal Brownian movement. This statistical parameter is generally used to describe the time-dependent phenomenon.

37. Each exchange needs a reciprocal situation and has a particular duration.