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Part 1: ECONOPHYSICS: History and introduction

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kurtosis 0. What to notice first: distribution. non-Gaussian. pronounced fat tails ... kurtosis 3. up-down asymmetry. skewness 0. R. Cont: Quantitative ... – PowerPoint PPT presentation

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Title: Part 1: ECONOPHYSICS: History and introduction


1
Part 1 ECONOPHYSICS History and introduction
  • Zoltán Eisler
  • Dept. of Theor. Phys., Budapest Univ. of
    Technology and Economics

2
PIGGY BANK World leaders in corporate finance
If you understand this, then we are
looking for you!
3
Solid facts
  • US 50 of fresh US theoretical physics graduates
    of major universities went to finance (1999)
  • Germany no prestigious bank without at least one
    small research group of physicists
  • Founded by physicists d-fine, Science Finance,
    Prediction Company, Volterra, Olsen (went
    bankrupt), etc.

4
Physicists in finance
  • Econophysics conferences
  • Budapest 1997, Palermo 1998, Dublin 1999, Liege
    2000, Tokyo 2000, Prague 2001, London 2001, Bali
    2002, Tokyo 2002, Warsaw 2003, Tokyo 2004
  • Journals
  • International Journal of Theoretical and Applied
    Finance
  • Quantitative Finance
  • special issues of Physica A

5
The birth of a science
  • Louis Bachelier (1870-1937)
  • Theorie de la Spéculation (1900)
  • PhD supervisor H. Poincaré
  • Theory of Brownian motion
  • GAUSSIAN distribution
  • Great influence

6
Nobel prize 1997
  • 1973 the revolutionary Black-Scholes formula
  • Based on
  • geometric Brownian motion
  • efficient market hypothesis (no perpetuum
    mobile)
  • Billions of USD invested

Myron Scholes
Robert Merton
7
Nevertheless...
  • 1998 Long Term Capital Management collapse
  • managed by Scholes
  • loss 2.5 billion

8
Nevertheless...
  • 1998 Long Term Capital Management collapse
  • loss 2.5 billion

9
Nobel prize 1990
Harry Markowitz Merton Miller
William Sharpe
  • Portfolio optimization
  • measure of risk standard deviation
  • Brownian motion

10
Non-Gaussian nature
  • 1963 Benoit B. Mandelbrot
  • non-Gaussian
  • many-s events come too often
  • Lévy distribution
  • Eugene Fama
  • random walk theory
  • applications

11
Monetary politics after WW II
  • 1944 Bretton Woods agreement
  • fixed exchange rate system for major currencies
  • fixed price of gold at 35 per ounce
  • enabled central bank intervention in currency
    markets
  • basis for WW II reconstruction
  • fast growth, full employment, stability, etc.
  • illusion of safety

12
Monetary politics after WW II
  • Vietnam 68
  • Watergate
  • Oil crisis, rising oil prices
  • 3rd World debt crisis
  • 1971 Nixon closes the gold window (103)

13
Monetary politics after WW II
  • Vietnam 68
  • Watergate
  • Oil crisis, rising oil prices
  • 3rd World debt crisis
  • 1971 Nixon closes the gold window (103)
  • Dramatic drop in SP 500
  • FX volatility increases from 6 to 40(!)
  • similar effect in raw material prices

14
Mid 70s New Era in Finance
  • RISK becomes high priority
  • Gold out of monetary interactions
  • Derivative markets flourish (decrease risk)
  • 1971 Intel presents first microprocessor

15
Mid 70s New Era in Finance
  • Risk becomes high priority
  • Gold out of monetary interactions
  • Derivative markets flourish (decrease risk)
  • 1971 Intel presents first microprocessor
  • Markets opened
  • International Money Market Chicago 1972
  • London International Future Exchange 1982
  • Deutsche Terminbörse 1990

16
Mid 70s New Era in Finance
  • Risk becomes high priority
  • Gold out of monetary interactions
  • Derivative markets flourish (decrease risk)
  • 1971 Intel presents first microprocessor
  • Markets opened
  • International Money Market Chicago 1972
  • London International Future Exchange 1982
  • Deutsche Terminbörse 1990

High benefit possibilities with high risk
17
Technological Revolution
  • Unforeseen developments
  • new branches emerge (high tech, services)
  • information technology, computers

18
  • Deregulation of markets
  • Ever rising speed and dropping cost of
    computation and data transfer
  • Computer networks
  • Increasing complexity

19
  • Financial industry, financial products
  • after mid-70s faster than exponential growth

20
  • Financial industry, financial products
  • after mid-70s faster than exponential growth
  • note the log-scale

21
Why Physics and Why Physicists?
  • Beware the facts!
  • Interplay between experiments, theory and
    simulations
  • Use of math and computing as flexible tools
  • Modeling extracting important features from
    complex phenomena
  • Physicist General Problem Solver

22
Why Statistical Physics?
  • Renormalization group theory
  • strongly interacting many-body systems,
    cooperative phenomena, etc.
  • New paradigms
  • non-linear dynamics (chaos theory)
  • disorder (percolation, spin glasses)
  • fractals, driven systems
  • Broad fields of applications
  • biology, social systems, networks, and...

23
Stock market
24
Stock market
Price of GE PGE(t) Logarithmic
price lnPGE(t) Logarithmic
return rGE(t)lnPGE(t) lnPGE(t-?t)
25
Stock market
Price of GE PGE(t) Logarithmic
price lnPGE(t) Logarithmic
return rGE(t)lnPGE(t) lnPGE(t-?t)
?t 10 sec...1 min...1 day
26
What to notice first basic stylized facts
  • non-Gaussian

27
What to notice first distribution
  • non-Gaussian
  • pronounced fat tails
  • kurtosis gt 0

28
What to notice first distribution
  • non-Gaussian
  • pronounced fat tails
  • kurtosis gt 3
  • up-down asymmetry
  • skewness lt 0

R. Cont Quantitative Finance 1, 223-236 (2000)
29
Convergence to a Gaussian
  • finite second moment
  • central limit theorem would ensure convergence to
    a Gaussian

L. Kullmann, J. Kertész et al. Int. J. Th. App.
Fin. 3, 371-373 (2000)
30
Convergence to a Gaussian
  • finite second moment
  • central limit theorem would ensure convergence to
    a Gaussian
  • surprisingly slow
  • returns are not uncorrelated!
  • ?t 1 week 1 year

L. Kullmann, J. Kertész et al. Int. J. Th. App.
Fin. 3, 371-373 (2000)
31
Autocorrelations
  • no serial autocorrelations beyond 10 minutes
  • non-linear functions of returns exhibit
    autocorrelation

R. Cont Quantitative Finance 1, 223-236 (2000)
32
Leverage autocorrelations
  • volatility often approximated by r(t)

Z.E., J. Kertész Physica A 343C, 603-622
33
Leverage autocorrelations
  • volatility often approximated by r(t)
  • past sign and future volatility (tgt0)

Z.E., J. Kertész Physica A 343C, 603-622
34
Leverage autocorrelations
  • volatility often approximated by r(t)
  • past sign and future volatility (tgt0)
  • volatility nervousness of the
    market

Z.E., J. Kertész Physica A 343C, 603-622
35
The term structure of returns
  • original idea simple Brownian motion
  • S(t) independent random variables

Z.E., J. Kertész Physica A 343C, 603-622
36
The term structure of returns
  • extension of the original idea of simple Brownian
    motion
  • A(t) strongly (power-law) correlated amplitude
    term (volatility), fat tails
  • S(t) uncorrelated sign term

Z.E., J. Kertész Physica A 343C, 603-622
37
The term structure of returns
instantaneous standard deviation
  • extension of the original idea of simple Brownian
    motion
  • A(t) strongly (power-law) correlated amplitude
    term (volatility), fat tails
  • S(t) uncorrelated sign term

Z.E., J. Kertész Physica A 343C, 603-622
38
Part 1 Summary
  • Brief history
  • Key words
  • returns
  • volatility
  • distribution of returns
  • correlations
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