Content uploaded by Panos Argyrakis

Author content

All content in this area was uploaded by Panos Argyrakis on Jan 07, 2015

Content may be subject to copyright.

207

Journal of Engineering Science and Technology Review 4 (3) (2011) 207 – 208

Special Issue on Econophysics

Note

What is EconoPhysics?

P. Argyrakis*

Dep. of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece.

___________________________________________________________________________________________

Abstract

I present some ideas of how EconoPhysics has come to life in the past few years, what it deals with, the main topics of

discussion in this community, and perhaps what can it offer in the future. One can see that the tools of Statistical Physics

can indeed be utilized properly to understand better the behavior of the markets by constructing mathematical functions

which use empirical/historical values. As the volume of such historical data explodes in recent years in an all-electronic

world, it has become more and more necessary to use such new tools, thus entering a new era in the financial world,

where computers play a very important role in decision making.

Keywords: EconoPhysics, probability distribution functions, correlation functions.

__________________________________________________________________________________________

1. EconoPhysics

During the past twenty or so years [1-5] there has been an

emergence of new approaches in mostly all sciences which

are based on the idea that practically all entities considered,

whether they are molecules, human relations, or prices of

goods, exist through some sort of interaction between the

multitude of their elements, which strongly affects their

overall behavior. Thus, a new picture based on graph theory

has spawned new ways to visualize nature, by casting these

elements as network nodes and their interactions as the links

(bonds) that connect these nodes. It is really amazing how in

such a short period of time a huge variety of applications

found their way in such pictures, and new ways were

generated to visualize old problems, thus improving their

understanding and/or offering explanations that were not

conceivable earlier. Economics is a science which was not

left out of this approach. It is a science that is trying to

assign the proper value to every item that people deal with in

our world. Of course, one can easily see that it is not related

at all to the quantities that we commonly meet in Physics or

the other Natural Sciences, i.e. the physical laws in nature.

Thus, one may naively ask what is the common element

between the two, how can they possibly be related, and what

has prevented it all along. This is a good question. The

answer is simple, it is that the values assigned to all goods of

the Economy are characterized by fluctuations. But

fluctuations constitute an inherent characteristic of all

natural measurements. It is a subject that is studied in

Statistical Physics in great detail. Thus, this common

characteristic constitutes the bridge between these two

disparate fields, which seemingly are concerned with so

different ideas. One would then hope to apply well known

methods from Statistical Physics to real-world data coming

from the economy, calculate equivalent quantities that one

has in Physics, but now using data such as prices of some

common instrument, instead of using data arising from

physical measurements. One would ask at first if this is

possible, and the quick answer is that indeed it is possible, as

it has been shown in a large number of cases recently.

What has additionally promoted such an approach is the

huge volumes of economic data that in the past few years

have been continuously generating. Of course, the reason for

this is the transition to all-electronic markets, making

possible to keep records of transactions at extremely small

time increments, of the order of msec, something unheard of

just a few years ago. This has necessitated on one hand the

use of powerful computers, and on the other hand the use of

powerful statistical methods in order to produce meaningful

pictures of the financial markets in a very short period of

time, and all this must be realized, of course, in real time.

The huge increase of the volume of currency trading, and the

introduction of derivatives in the 70s have all helped such

trends and necessitated new approaches for the financial

markets.

A first impetus to the statistical analysis of financial

markets was shown by the unexpected observation in the

behavior of the distribution of the price fluctuations of some

instrument. It can safely be assumed as a starting point that

price fluctuations occur at all scales and very importantly

they are random, i.e. prices in any time increment are not

correlated. This was proposed over 100 years ago as an

empirical result and it was commonly accepted. If this is true

one would expect intuitively to have a Gaussian or Normal

distribution for the changes of the price of a stock. Recent

results in the last two decades showed that this is not so.

While the line shape around the maximum value of the

distribution of price changes seems to be correct, the shape

at the two extremes (the two tails) do not obey a Gaussian at

all, but rather they agree with a Levy distribution, which

JOURNAL OF

Engineering Science and

Technology Review

www.jestr.org

______________

* E-mail address: panos@physics.auth.gr

ISSN: 1791-2377 2011 Kavala Institute of Technology. All rights reserved.

P. Argyrakis /Journal of Engineering Science and Technology Review 4 (3) (2011) 207-208

208

falls much more sharply at the ends (rather than having long

tails that go asymptotically to zero as in the Gaussian).

As mentioned earlier, in financial markets one is not

interested only in the price itself, but also in the fluctuations

of this price, which is usually called the volatility in the

price. At periods of extreme volatility it is when huge market

gyrations occur, such as market crashes, i.e. very sharp

changes in a very short period of time, such as the one on

October 1987 when the main market indices in USA fell by

over 20% in one day. Conceivably, the same could happen

in large upswing changes, for symmetry reasons, even

though historically this is not true. Such changes belong to

the tails of the distributions, which as mentioned above are

far from Gaussian. Actually, if they were Gaussian, then the

1987 market crash would have a probability of 10-135 to

happen, the inverse of which is larger than the size of the

universe. Thus, it is now clear that the behaviors of the tails

of such distributions are far from random, even though the

prices themselves could be taken to be random. The

interplay of these two quantities (i.e. the price of an

instrument and the volatility of this price) is still a very

active field of research, where no definite answers have

emerged.

Such sharp changes as described above belong to the

class of the so-called "rare events", which are events that

happen very rarely in the world, but when they happen they

have a very large impact on people. Such events could be,

for example, a very large earthquake, a powerful tsunami, a

catastrophic nuclear accident, or a huge swing in the

financial markets discussed above. Such events may occur

only once or twice within a lifetime, or let us say that they

have a frequency (roughly) of the order of a century. The

question then is if they can be predicted or if any

information about them can be obtained ahead of time, as for

example, if they have any precursors. Actually, this is the

holy grail of the markets, for obvious reasons. I will give

some simple arguments which I believe show that this is not

possible to do. One wants to believe that we all live in a

world of efficient markets. This hypothesis states that no

matter how complex markets are, valuations are made in a

rational way, which means that they are based on the supply-

demand ratio. It also states that all players have all the

available information in all parts of the world, so that if

some form of arbitrage may temporarily take place, soon it

will be smoothened out exactly by the same forces that have

generated it and by the same mechanism. Equivalently, it is

palatable to assume that if any such precursor would emerge,

then the market forces would immediately take effect,

making this precursor useless. Who would buy a stock if it is

known that tomorrow it will be half price and the day after

quarter-price? If such a real precursor would exist, then this

would in effect shut down the market. For a market to

operate smoothly, it is by definition required to have both

buyers and sellers. When one of the two ceases to exist, then

the market simply cannot operate at all. The market is not an

infinite bath of financial instruments which are traded

between a customer and the market. The market is simply a

mechanism of matching buyers and sellers, therefore, if a

catastrophic change takes place, then the balance between

buyers and sellers is strongly disturbed, making trading

impossible. With these thoughts, one can see that (almost by

definition) such indications as predicting bubble bursts,

finding precursors, etc. do not make any sense in a normal

market. But just like with all other human behavior in

history claims to the opposite abound and will do so in the

future, because it is part of human nature.

Another property of interest is the correlation between

two or more financial instruments. By this term it is simply

meant how does the change in one instrument depend on the

change in another. For example, if we have two stocks, how

does the rise or fall of one compare to the behavior of the

other in the same time period. It is well known that in daily

fluctuations typically most stocks move in unison, this is

true at least for the large valuation stocks, such as the ones

contained in the DJ Industrials. Also, the same may be true

for stocks that belong to some particular sector, such as for

example, oil industry, or banking, etc. One wants to know

more in detail the quantitative behavior of these stocks.

Thus, it is possible to calculate the so called correlation

coefficient, which answers this question. The correlation

coefficient is a function similar to the correlation function,

which gives, for example, the relative positions or velocities

of particles in a physical system.

Finally, an area where methods from Physics can

contribute is the estimation of risk and the creation of an

optimal portfolio. These ideas have come to the forefront

more so in recent years because of the increase of derivative

trading. As we know derivatives carry a much larger risk

than stocks themselves. Because they involve in addition to

the valuation of the underlying instrument, the parameter of

time and volatility, estimating their fair value is not an easy

task. Probability theory used in physical processes can aid

significantly at this point, for which there is still no general

consensus. Important seminal results as the Black-Scholes

theory for option pricing do not agree with empirical, real

prices even today.

Summarizing, Physics can contribute to Economics by

lending the mathematical tools that have been developed

over the years for the study of atoms and molecules. These

mainly include probability distribution functions and

correlation functions. Large volumes of historical data exist

today that include among others, prices of stocks,

derivatives, such as options, commodities, currency pairs,

index of inflation, income distribution, import-export of

goods between countries, etc. to name only a few. Such

functions as the ones mentioned above may give a better

understanding of the mechanism that governs their behavior.

It is not expected that EconoPhysics will revolutionize

Economics or be able to predict trends in the Economy. But

experience has shown that interdisciplinary approaches are

always useful for the advancement of knowledge.

______________________________

References

1. R. N. Mantegna and H. E. Stanley, “An Introduction to

Econophysics: Correlations and Complexity in Finance”,

Cambridge University Press, (2000).

2. J. L. McCauley, “Dynamics of Markets: Econophysics and

Finance”, Cambridge University Press, (2004).

3. J. P. Bouchaud and M. Potters, “Theory of Financial Risks: From

Statistical Physics to Risk Management”, Cambridge University

Press, (2000).

4. D. Sornette, “Why Stock Markets Crash: Critical Events in

Complex Financial Systems”, Princeton University Press, (2003).

5. B. Mandelbrot and R. L. Hudson, “The (Mis)Behavior of Markets:

A Fractal View of Risk, Ruin and Reward”, Basic Books, (2004).