Part 1: ECONOPHYSICS: History and introduction

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Part 1 ECONOPHYSICS History and introduction

• Zoltán Eisler
• Dept. of Theor. Phys., Budapest Univ. of
  Technology and Economics

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PIGGY BANK World leaders in corporate finance
If you understand this, then we are
looking for you!
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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.

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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

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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

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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
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Nevertheless...

• 1998 Long Term Capital Management collapse
• managed by Scholes
• loss 2.5 billion

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Nevertheless...

• 1998 Long Term Capital Management collapse
• loss 2.5 billion

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Nobel prize 1990
Harry Markowitz Merton Miller
William Sharpe

• Portfolio optimization
• measure of risk standard deviation
• Brownian motion

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Non-Gaussian nature

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

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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

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Monetary politics after WW II

• Vietnam 68
• Watergate
• Oil crisis, rising oil prices
• 3rd World debt crisis
• 1971 Nixon closes the gold window (103)

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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

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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

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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

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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
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Technological Revolution

• Unforeseen developments
• new branches emerge (high tech, services)
• information technology, computers

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

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

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

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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

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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...

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Stock market
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Stock market
Price of GE PGE(t) Logarithmic
price lnPGE(t) Logarithmic
return rGE(t)lnPGE(t) lnPGE(t-?t)
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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
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What to notice first basic stylized facts

• non-Gaussian

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What to notice first distribution

• non-Gaussian
• pronounced fat tails
• kurtosis gt 0

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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)
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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)
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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)
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Autocorrelations

• no serial autocorrelations beyond 10 minutes
• non-linear functions of returns exhibit
  autocorrelation

R. Cont Quantitative Finance 1, 223-236 (2000)
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Leverage autocorrelations

• volatility often approximated by r(t)

Z.E., J. Kertész Physica A 343C, 603-622
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Leverage autocorrelations

• volatility often approximated by r(t)
• past sign and future volatility (tgt0)

Z.E., J. Kertész Physica A 343C, 603-622
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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
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The term structure of returns

• original idea simple Brownian motion
• S(t) independent random variables

Z.E., J. Kertész Physica A 343C, 603-622
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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
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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
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Part 1 Summary

• Brief history
• Key words
• returns
• volatility
• distribution of returns
• correlations