Econophysics
B.Sc. 4th Year
Prakash Chanda Gupta
What is Econophysics?
The econophysics is the physics that deals with the
dynamical and stochastic process in finance and
economics. Mostly we use ideas of statictical physics
to describe the economical behaviours, so it is also
called statictical econimics. The econophysics is
probabilistic in nature.
Motivation – Revolution in market
• First Revolution
In 1970s, a series of significant changes has taken in the world of finance. One key
year was 1973, when currencies began to be traded in financial markets and their
values determined by the foreign exchange market, a financial market active 24
hrs a day all around the world. During the same year, Black and Scholes published
the first paper that presented a rational option pricing formula. In the same
decade, the foreign currencies entered in the markets as a financial assets.
People’s stated to buy and sell the foreign currencies and the exchange rates
started to be affected by the market. This brought first revolution in the financial
market.
Motivation – Revolution in market
• Second Revolution
In the 1980s the financial data, the data corresponding to foreign
exchange market entered into the revolutionary computerera. People
started to store and analyze the data and predict market. Electronic
storing of data relating to financial contracts or (to prices at which traders
are willing to buy or sell) and sharing of data made it more easier and
faster to predict and analyze the future behaviour of market and nature of
loss and gain.This brought 2nd revolution in the financial market.
Financial Terms
• High frequency data
The data in which the time lapse in between two data points is vey small is called high
frequency data. Example: Financial data
• Derivative product
The financial asset which is derived from some other assets but have different property than
original asset is called derivative product. Example: Bread, car computer etc.
• Financial Asset
Any thing or idea that can be sold in market is called finacial asset.
• Bid quotes and ask quotes
The price of financial asset at which some one is willing tosell that asset is called Bid quotes.
The Price of financial assets at which someone is willing to buy is called ask quotes.
• Option – pricing
Options are derivative contracts that gives the holder the right but no obligation to buy or sell
the underlying financial assets at a specified price or after some period of time.
Pineering Approach in Econophysics
People have been trying to model complete system like pattern
formation in organism, price change in market rate of income in
business etc. In order to describe the observed behaviour of data in
the financial market, many People have tried different types of
approaches. Some of the pioneering approaches in Econophysics are
discussed next.
Pioneering approaches in Econophyiscs
• Power law distribution
It was first use in socioeconomic sector even before using it in natural
science like physics. People in natural science were sceptic about it
because this distribution lacks characteristics length. In statistics a
power law is a functional relationship between two quantities where a
relative change in one quantity results in a proportional relative
change in other quantity, independent of initial size of these
quantities; one quantity varies as a power of another.
Pioneering approaches in Econophyiscs
• Random Walk and Bachlier Model
A random walk is a mathematical formalization of path that consists of
succession of random steps. Example: the path traced by a molecule as it
travels in a liquid or gas. In natural science very light particle suspended in
fluid perform random walk. This means their trase are undetermined and rule
by stochastic process. Einstein in 1905 used random walk model to describe
Brownian motion but before that Bachelier had used it to discuss the
distribution of price change in stock market.
Pioneering approaches in Econophyiscs
• Distribution of Price Change
Bachelier’s attempted to find the distribution of price change and proposed a
Gaussian model, which was not motivated to the depth in mathematical science. His
model was soon replaced by model in which the stock and the stock price are log-
normal distributed. That means stock price for geometric Brownian motion. In a
geometric Browian motion the difference of logarithm of price are Gaussian
distributed. This provide for order approximation to what ordered in real data. As the
geometrical Brownian model was also inadequate, other served models has been
proposed to address the observed time fluctuation of second moment of price change
and flat tail-distribution.
Pioneering approaches in Econophyiscs
• Mandelbrot’s Hypothesis
According to his hypothesis price changes as follows a levy stable
distribution. Levy stable processes are stochastic processes obeying
general central limit theorem. But this model has also loop holes. A
levy distribution 𝑝 𝑥 = 𝑥
! "#$
with 𝑥 < 2 have infinite variance.
The Chaos approach
The widely accepted belief in financial theory is that time series of asset prices are
unpredictable. This belief is the corner stone of the desription of price dynamics as
sochastic process.
The process which are extremely sensitive to the initial condition are called the
chaotic process, they are highly nonlinear process.
It is believed in financial theory that time series of assets price are unpredictatble.
According to chaos theory, the unpredictable time series can arise from deterministic
non-linear systems which differ from stochostic process.
The Chaos approach
The goal of non-linear dynamics has been to reconstruct the attractor present
in the chaotic time evolution and to measure its dimension d. But this is very
demanding job. As the financial data is of very high dimension it is almost
impossible to describe it (price change) using finite dimensional model.
Although, it cannot be ruled out that financial market follow chaotic
dynamics, we choose to work, within a paradigm. It is because of financial
data is very very high dimensional and it is unlikely to us to take care of all
the factors that affect the market.
Characteristics Length
Charateristics length of any function is the interval in the variable
which retains the property of that physical phenomenon.
For example ,
%&
%'
= 𝑁
(
𝑒
!'/*
z is the characteristics length which gives the amount of substance
(atom) that remains unaffected after time t = z to be
&
!
+
Recent trends in econophysics
The journey of Physicists in the economic has root on the majarancies
paper published on 1936. The essential analogy between statistics and
social science. Only a very few no. of physicists were interested in the
topic of econophysics in the early days. But recently a growing no of
Physicists have attempted to analyze model and interprete the financial
market and more generally the economical behaviours.
Recent trends in econophysics
Financial markets are open systems in which many subunits interact in
non-linear way in the presence of feedbacks. In financial markets, the
governing rules are rather stable and time evolution is continously
monitored. It is very difficult to do original large scale experiment in
econophysics. But a very large database of market already available
enable econophysicists to do emperical experiment. So it is how possible
to develop hypothetical experimental models and test their accuracy and
predict power using existing data.
Recent trends in econophysics
The main problems in quantitative finance are in “fundamental aspects” related to
the nature of the random process of assets and ”technical aspects” related to the
solution of option pricing problem obtained under the ass umption that the underlying
assets performs the proposed random process.
Since 1990 a good number of physicists are being in the science of market. The
fundamental difference between physicists approach from that of econimist is that
physicists put emphoric on the empirical analysis. But some people argue that the
emperical experiment in the financial data is not equivalent to the experiments in
other natural sciences.
Recent trends in econophysics
The maintrends in econophysics are the following:
1. The complete statistical characteristics of the stochastic of price changes.
2. Determining of shape of the financial assets.
3. The temporal memory of financial data.
4. Development of theoretical model that is able to encompass all the essential features of real market.
5. Rational pricing of derivative product.
6. Analogies and difference between price dynamic in financial market and such process in turbulatory system and ecological system.
7. Income distribution of firms and statistical properties of their growth rate.
8. The statistical properties of performances of complex organizations such as universities or entire country.
9. Time correlation, auto correction and dimension of attractor is based on price distribution of assets.
