## The Statistical Mechanics of Financial MarketsThese book grew out of a course entitled "Physikalische Modelle in der Fi nanzwirtschaft" which I have taught at the University of Freiburg during the winter term 1998/1999, building on a similar course a year before at the University of Bayreuth. It was an experiment. My interest in the statistical mechanics of capital markets goes back to a public lecture on self-organized criticality, given at the University of Bayreuth in early 1994. Bak, Tang, and Wiesenfeld, in the first longer paper on their theory of self-organized criticality [Phys. Rev. A 38, 364 (1988)] mention Mandelbrot's 1963 paper [J. Business 36, 394 (1963)] on power-law scaling in commodity markets, and speculate on economic systems being described by their theory. Starting from about 1995, papers appeared with increasing frequency on the Los Alamos preprint server, and in the physics literature, showing that physicists found the idea of applying methods of statistical physics to problems of economy exciting and that they produced interesting results. I also was tempted to start work in this new field. However, there was one major problem: my traditional field of research is the theory of strongly correlated quasi-one-dimensional electrons, conducting polymers, quantum wires and organic superconductors, and I had no prior education in the advanced methods of either stochastics and quantitative finance. |

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### Contents

1 | |

Basic Information on Capital Markets | 11 |

Random Walks in Finance and Physics | 23 |

The BlackScholes Theory of Option Prices | 47 |

Scaling in Financial Data and in Physics | 79 |

Turbulence and Foreign Exchange Markets 125 | 124 |

Risk Control and Derivative Pricing | 139 |

Microscopic Market Models | 159 |

Theory of Stock Exchange Crashes | 185 |

Notes and References | 213 |

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agents analysis arbitrage assumed assumption Bachelier Bachelier's behavior Black–Scholes bond Bouchaud call option Chap correlations courtesy crash depends derivative diffusion discussed distribution function Dow Jones drift earthquakes evolution expectation value exponent financial data financial markets financial time series finite foreign exchange markets forward contract futures Gaussian distribution geometric Brownian motion hedging important interest rate investment investors Lévy distributions Lévy flight log-normal long position martingale maturity noise traders observed option prices parameters Phys physics portfolio power law prediction price changes price histories price movements probability density function probability distribution problem profit put option random numbers random variables random walk real markets Reprinted rescaling returns risk risk-free riskless Sect sell orders shown in Fig shows solid line Sornette speculative stable Lévy distributions standard deviation statistical mechanics stochastic process stock market stock price strategy tails term theory tion trading turbulence underlying security variance volatility Wiener process zero