sign in sign up
<<
Home , Econophysics, Mathematical finance, Statistical finance, Statistical physics

1

Econophysics: A Brief Review of Historical Development, Present Status and Future Trends.

B.G.Sharma Sadhana Agrawal Department of and Computer , Department of Physics Govt. Science College Raipur. (India) NIT Raipur. (India) [email protected] [email protected]

Malti Sharma WQ-1, Govt. Science College Raipur. (India) [email protected]

D.P.Bisen SOS in Physics, Pt. Ravishankar Shukla University Raipur. (India) [email protected]

Ravi Sharma Devendra Nagar Girls College Raipur. (India) [email protected]

Abstract: The conventional economic 1. Introduction: approaches explore very little about the dynamics of the economic systems. Since such How is the like the cosmos systems consist of a large number of agents or like the nucleus of an ? To a interacting nonlinearly they exhibit the conservative , or to an , properties of a . Therefore the the question sounds like a joke. It is no tools of and nonlinear laughing matter, however, for dynamics has been proved to be very useful Econophysicists seeking to plant their flag in the underlying dynamics of the system. In the of . In the past few years, this paper we introduce the concept of the these trespassers have borrowed ideas from multidisciplinary field of , a , , and other neologism that denotes the activities of accomplishments of physics in an attempt to who are working on economic explore the divine undiscovered laws of problems to test a variety of new conceptual . They are already tallying what they approaches deriving from the physical science say are important gains. The tools of physics and review the recent developments in the provide an ideal background for discipline and possible future trends. approaching problems in economics [1]. Physics training, gives a person powerful Key Words: Econophysics, Stistical Finance, mathematical tools, computer savvy, a Physics of Finance facility in manipulating large sets of data, and an intuition for modeling and Broad Area: Physics simplification. Such skills have brought a new order into economics. Sub Area: Econophysics

2

2. What lies in Econophysics? Reliance on models based on incorrect axioms has clear and large effects [2]. The Econophysics is an interdisciplinary research Black-Scholes model assumes that changes field, applying theories and methods originally have a Gaussian , i.e. the developed by physicists in order to solve of extreme events is deemed negligible. problems in economics, usually those including Unwarranted use of this model to the or processes and nonlinear downfall on stock markets spiraled into the dynamics. Its application to the study of financial October 1987 crash. Ironically, it is the very use markets has also been termed of the crash-free Black-Scholes model that referring to its roots in statistical physics. destabilized the market! In the recent subprime Physics has played an important role in the crisis of 2008 also, the problem lay in part in the development of economic theory through the development of structured financial products that 19th century, and some of the founders of packaged sub-prime risk into seemingly neoclassical economic theory, were originally respectable high-yield . The models trained as physicists. used to price them were fundamentally flawed: they underestimated the probability of the multiple borrowers would default on their loans 2.1 Why Econophysics? simultaneously. In other words, these models again neglected the very possibility of a global The quantitative success of the crisis, even as they contributed to triggering one. economic is disappointing when it is Surprisingly, there is no framework in classical compared with that of physics. Its recurrent economics to understand wild markets, even inability to predict and avert crises, including the though their existence is so obvious to the current worldwide credit crunch is obvious? layman. Physicists, on the other hand, has Why is this so? Of course, modeling the madness developed in physics, several models allowing of people is more difficult than the motion of one to understand how small perturbations can planets, as Newton once said. But the goal here lead to wild effects. The theory of , is to describe the behavior of large populations, developed in the physics literature over the last for which statistical regularities should emerge. thirty years, shows that although a system may The crucial difference between physical sciences have an optimum state (such as a state of lowest and economics or financial is rather , for example), it is sometimes so hard to the relative role of concepts, equations and identify that the system in fact never settles empirical data. is built on there. This optimal solution is not only elusive, it very strong assumptions that quickly become is also hyper-fragile to small changes in the axioms: the rationality of economic agents, the environment, and therefore often irrelevant to invisible hand and market efficiency, etc. understanding what is going on. There are good Physicists, on the other hand, have learned to be reasons to believe that this complexity paradigm suspicious of axioms and models. If empirical should apply to economic systems in general and observation is incompatible with the model, the financial markets in particular. Simple ideas of model must be trashed or amended, even if it is equilibrium and linearity do not work. We need conceptually beautiful or mathematically to break away from classical economics and convenient. So many accepted ideas have been develop altogether new tools, as attempted in a proven wrong in the that still patchy and disorganized way by behavioral physicists have grown to be critical and queasy and econophysicists. But their fringe about their own models. Unfortunately, such endeavour is not taken seriously by mainstream healthy scientific revolutions have not yet taken economics. hold in economics, where ideas have solidified Thus there is a crucial need to into dogmas. In reality, markets are not efficient, change the mindset of those working in humans tend to be over-focused in the short-term economics and . They need and blind in the long-term, and errors get to realize that an overly formal and dogmatic amplified through social pressure and herding, education in the economic sciences and financial ultimately leading to collective irrationality, mathematics is serious part of the problem. In panic and crashes. Free markets are wild sum the Economic curriculums need to include markets. It is foolish to believe that the market more natural science so that it can tackle the real can impose its own self-discipline. world problems more accurately and efficiently.

3

2.2 Historical Development: speculative markets, an activity that is extremely important in fancial markets (1900). In 1938, Econophysics studies were started in the Ettore Majorana pre-sciently outlined both the mid 1990s by several physicists working in the opportunities and pitfalls in applying statistical subfield of [3-5]. They physics method to socio economic systems. Jan decided to tackle the complex problems posed by Tinbergen, who studied physics with Paul economics, especially by financial markets. Ehrenfest at Leiden University, won the Unsatisfied with the traditional explanations of first Nobel Prize in economics in 1969 for economists, they applied tools and methods from having developed and applied dynamic models physics - first to try to match financial data sets, for the analysis of economic processes. Ingrao and then to explain more general economic and Israel showed that the works of Léon Walras phenomena. With the availability of huge and on equilibrium economics is, amounts of financial data, starting in the 1980s, in fact, based on the physical concept it became apparent that traditional methods of of mechanical equilibrium. One of the most analysis were insufficient. Standard economic revolutionary development in the theory of methods dealt with homogeneous agents and speculative since Bachelier's initial work, equilibrium, while many of the interesting is the Mandelbrot's hypothesis that price changes phenomena in financial markets fundamentally follow a Levy rather than a depended on heterogeneous agents and far-from- Gaussian one. A widely accepted belief in equilibrium situations. financial theory is that of asset prices The term “econophysics” was coined by H. are unpredictable. Poincare (1854-1912) has Eugene Stanley in the mid 1990s, to describe the pointed the possibility of unpredictability in a. large number of papers written by physicists in nonlinear , establishing the the problems of stock and other markets, and foundations of the chaotic behavior. The study of first appeared in a conference on statistical chaos turned out to be a major branch of physics in Calcutta in 1995 and its following . It was only a question of publications. The inaugural meeting on time, how fast these ideas will start to appear in Econophysics was organised 1998 economy. Ironically, Poincare, who did not in Budapest by János Kertész and Imre Kondor. appreciate Bachelier's results, made himself a large impact on real complex systems as one of Though the term “Econophysics” has the discoverers of chaotic behavior in dynamical been entered the scientific language only about systems. Nowadays studies of chaos, self- one and half decade ago, the connection and organized criticality, cellular automata and interplay between physics and economy are neural networks are seriously taken into account, about 300 years old [6-8]. Literature is full of as economical and financial tools. examples of famous physicist’s involvement in economic or financial problems. Daniel The next major factor, changing the Gaussian Bernoulli introduced the idea of to world was a computer. First, it has changed the describe people's preferences (1738). Pierre- speed and the range of transactions drastically. Simon Laplace, in his Essai philoso-phique sur The application of computer started involuntarily les probabilites pointed out that events that to serve as an amplifier of fluctuations. Second, might seem random and unpredictable in the economies and markets started to watch each economics can be quite predictable and can be other more closely, since computer possibilities shown to obey simple laws (1812). Adolphe allowed for collecting exponentially more data. Quetelet further amplified the Laplace's ideas by In this way, several nontrivial couplings started studying the existence of patterns in data sets to appear in economical systems, leading to ranging from economic to social problems. nonlinearities. Nonlinear behavior and (1835). , originally trained as overestimation of the Gaussian principle for physicists, and a student of Willard Gibbs played fluctuations were responsible for the Black an important role in the development of Monday Crash in 1987, and the crisis in August, neoclassical economic theory. The first and September 1998 and sub-prime crisis of formalism of (a mathematical 2008. That shock had however also a positive model of efficient markets) was not in a impact visualizing the- importance of the non- publication by Einstein, but in Doctoral thesis by linear effects. Poincare has long ago pointed the Luis Bachelier. His work dealt the first possibility of unpredictability in a nonlinear formulation of the pricing of options in dynamical system, establishing the foundations 4 of the chaotic behavior. The study of chaos welcome mats for physicists over a decade ago. turned out to be a major branch of theoretical People with physics Ph.D.s hold about half of the physics. It was only a question of time, how fast so-called quantitative analyst positions at such these ideas will start to appear in economy. institutions, and they significantly outnumber Ironically, Poincare, who did not appreciate economists. Wall Street physics has been mostly Bachelier's results, made himself a large impact a proprietary pursuit of new spins on old on real complex systems as one of the methods for concocting abstract financial discoverers of chaotic behavior in dynamical instruments, of which stock options are among systems. Nowadays studies of chaos, self- the simplest examples. In the margins, a few organized criticality, cellular automata and physicist-financiers are working on so-called neural networks are seriously taken into account, black box trading schemes. as economical and financial tools. One of the benefits of the computers was that economic Now, the embrace of physics and finance has systems started to save more and more data. been reached into academics. Physicists at Today markets collect incredible amount of data. universities are taking up finance, and This triggers the need for new methodologies, nonacademic physicists in finance are pursuing able to manage the data. In particular, the data basic research. Together they published about started to be analyzed using methods, borrowed more than 100 economics papers last year in widely from physics, where seeking for journals of physics and the number is increasing regularities and for unconventional correlations exponentially yoy. Currently, the almost regular is mandatory. In the last fifteen years, several meeting series on the topic include: educational and research institutions devoted to Econophysics Colloquium, ESHIA/ WEHIA, study of complexity launched the research ECONOPHYS-KOLKATA, APFA. Participants programs in economy and financial engineering. in the movement say that research in finance is These studies were devoted mostly to growing faster than in any other area of physics. quantitative finance. To a large extent, it was Within the dark recesses of proprietary financial triggered by vast amount of data accessible in research on and off Wall Street, an unreckoned this field but purportedly small number of stock analysts are building what they call black boxes. These 2.3 Present Status: computerized systems monitor current and past prices of a stock or asset, consult Recently, a growing number of exchange rates or other factors that might serve physicists have attempted to analyze and model as financial indicators, and spit out decisions financial markets and, more generally, economic from moment to moment about whether an systems [6]. This unorthodox point of view was investor should buy or sell. An ever-evolving considered of marginal until recently. formula instructs some black boxes as to which Indeed, prior to the 1990s, very few professional indicators to consult and how to factor them into physicists did any research associated with social the decisions. The boxes themselves may devise or economic systems. Since 1990, the physics these formulas. Many boxes evaluate research activity in this field has become less using programming that mirrors how brain-cell episodic and a research community has begun to networks operate. The computers effectively emerge. The research activity of this group of teach themselves as they go along how to physicists is complementary to the most forecast swings in price. However, the goal of traditional approaches of finance and black box research is narrow. Researchers have a . One characteristic strong disincentive to publish any innovations difference is the emphasis that physicists put on that would be useful for turning profits, since if the empirical analysis of economic data. Another everybody knew of them, they would cease to is the background of theory and method in the work. field of statistical physics developed over the past three decades that physicists bring to the This brief presentation of some of the current subject. The concepts of scaling, universality, efforts in this emerging discipline can be disordered frustrated systems, and self-organized summarized as follows: systems might be helpful in the analysis and modeling of financial and economic systems. Financial firms on Wall Street in U.S.A. put out 5

2.3.1. Statistical characterization of the 2.3.4. Time correlation of a financial of price changes of a series: financial asset: One common theme encountered in Among the important areas of physics these research areas is the time correlation of a research dealing with financial and economic financial series. The detection of the presence of systems, one concerns the complete statistical a higher-order correlation in price changes has characterization of the stochastic process of price motivated a reconsideration of some beliefs of changes of a financial asset. Several studies have what is termed '. been performed that focus on different aspects of the analyzed stochastic process, e.g., the shape of 2.3.5. Income distribution of firms and the distribution of price changes, the temporal their growth : memory, and the higher-order statistical properties . This is still an active area, and In addition to the studies that analyze attempts are ongoing to develop the most and model financial systems, there are studies of satisfactory stochastic model describing all the the income distribution of firms and studies of features encountered in empirical analyses. One the statistical properties of their growth rates. important accomplishment in this area is an The statistical properties of the economic almost complete consensus concerning the performances of complex organizations such as finiteness of the second moment of price universities or entire countries have also been changes. This has been a longstanding problem investigated . in finance, and its resolution has come about because of the renewed interest in the empirical study of financial systems. 3. Impact on and finance:

2.3.2 development of a theoretical Papers on econophysics have been model: published primarily in journals devoted to physics and statistical mechanics, rather than in A second area concerns the leading economics journals. Mainstream development of a theoretical model that is able to economists have generally been unimpressed by encompass all the essential features of real this work. Some Heterodox economists, financial markets. Several models have been including Mauro Gallegati, and Paul proposed , and some of the main properties of Ormerod, have shown more interest, but also the stochastic dynamics of stock price are criticized trends in econophysics. reproduced by these models as, for example, the In contrast, econophysics is having some impact leptokurtic 'fat-tailed' non-Gaussian shape of the on the more applied field of quantitative finance, distribution of price differences. Parallel whose scope and aims significantly differ from attempts in the modeling of financial markets those of economic theory. Many econophysicists have been developed by economists. have introduced models for price fluctuations in financial markets or original points of view on 2.3.3. of a established models. products:

4. Conclusion : Other areas that are undergoing intense investigations deal with the rational pricing of a derivative product when some of the canonical Knowledge of dynamical properties of assumptions of the Black & Scholes model are economic systems is essential for fundamental relaxed and with aspects of portfolio selection and applied reasons. Such knowledge is crucial and its dynamical optimization. A further area of for the building and testing of a model of research considers analogies and differences economic market. Dynamics enters the between price dynamics in a economics in two quite different and and such physical processes as turbulence and fundamental ways. The first, which has its ecological systems . counterpart in the natural sciences, is from the fact that the present depends upon the past. Such models typically are of the form 6

markets as mediators of communication and dis- yt = f (yt-1) tributed computation, which underlie the collective processes of price formation and where we consider just a one period lag (a allocation of resources, and the emergence of the Markov process). The second way dynamics social institutions that support those functions, enters , which has no are quintessentially economic phenomena. Yet counterpart in the natural sciences, arises from the notions of markets' communication or the fact that economic agents in the present have computational capacities, and the way expectations (or beliefs) about the future. Again differences in those capacities account for the taking a one-period analysis, and denoting the stability and historical succession of markets, present expectation about the variable y one may naturally be part of the physical world with period from now by E yt+1, then its human . Markets and other economic institutions bring with them concepts y,=g(Eyt+1) of efficiency or optimality in satisfying human desires. While intuitively appealing, such ideas Let us refer to the first lag as a past lag and the have proven hard to formalize even if some second a future lag. There is certainly no reason progress has been made. As with most new areas to suppose modeling past lags is the same as of physical inquiry, we expect that the ultimate modeling future lags. Furthermore, a given goals of a physical economics will be declared model can incorporate both past lags and future with hindsight, from successes in identifying, lags. The natural sciences provide the measuring, modeling, and in some cases mathematics for handling past lags but has predicting empirical regularities. One argument nothing to say about how to handle future lags. It that is sometimes raised at this point is that an is the future lag which gained most attention in empirical analysis performed on financial or the 1970s, most especially with the rise in economic data is not equivalent to the usual . Once a future lag enters a experimental investigation that takes place in model it becomes absolutely essential to model physical sciences. In other words, it is im- expectations, and at the present time there is no possible to perform large-scale experiments in generally accepted way of doing this. This does economics and finance that could falsify any not mean that we should not model expectations, given theory. rather it means that at the present time there are a We note that this limitation is not specific to variety of ways of modeling expectations, each economic and financial systems, but also affects with its strengths and weaknesses. This is an area such well developed areas of physics as for future research. In spite of a long effort, this , , and goal has not yet been achieved. Statistical and . Hence, in analogy to activity in Theoretical physicists can contribute a lot to the these more established areas, we find that we are resolution of these scientific problems by sharing able to test and falsify any theories associated , with researchers in the other disciplines with the currently available sets of financial and involved, the background in , economic data provided in the form of recorded disordered systems, scaling, and universality that files of financial and economic activity. has been developed over last 30 years. Despite the field’s long history of association, the sub- stantial contribution of physics to economics is still in an early stage, and we think it fanciful to Appendix: predict what will ultimately be accomplished. Almost certainly, "physical" aspects of theories Some Important Centers of Econophysics of social order will not simply recapitulate Research: existing theories in physics, though already there appear to be overlaps. The development of 1. Boston University USA. economies can be contingent on accidents of 2. USA history and at every turn hinges on complex 2. Saha Institute of , Kolkata, aspects of human behavior. India. Nonetheless, striking empirical regularities 3. Ecole Centrale Paris, France. suggest that at least some social order is not 4. University of Maryland, UK. historically contingent, and is perhaps 5. University of Palermo, Italy. predictable from first principles. The role of 7

References: chaotic Behavior, Int. Res. Jr. of Lab to Lands, Vol.1 No. IV, Oct- Dec. (2009)266- 270 [1]. R. N. Mantegna and E. H. Stanley, An [7]. Balgopal Sharma, Study of the Multifractal Introduction to Econophysics, Cambridge behavior of NIFTY using Detrended University Press (2004) Fluctuation Analysis ,ECONOPHYS- [2]. J.P.Bouchad, May 2, 1998 EUROPEAN KOLKATA V : International Workshop on PHYSICAL JOURNAL B[2] May 2, (1998) Econophysics of order driven markets, 9-13 [3]. J.P.Bouchad and M.Potters, Theory of March 2010. Financial : From Statistical Physics to http://www.saha.ac.in/cmp/epkol , Cambridge University 05.2010/abstracts.html Press(2000) [8]. B.G. Sharma, Application of Multiscale [4]. B.G.Sharma Lecture on Econophysics, analysis to verification of the Govt. Girls Degree College Ambikapur(27 applicability of Efficient market hypothesis, jan 2007). Econophysics Colloquium 2010 ,November [5]. J.D.Farmer, Market Force, Ecology, and 4-6, 2010 in Taipei, Taiwan Evolution, Adap-Org preprint server http://www.phys.sinica.edu.tw/~socioecono/ 9812005. econophysics2010/pdfs/SharmaBGPap [6]. B.G.Sharma, D.P.Bisen, Ravi Sharma and er.pdf. Malti Sharma, Application of Nonlinear Dynamics to and its