## The Statistical Mechanics of Financial MarketsThe present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are due to my practical experience as a risk manager in the German Savings Banks’ As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added. The chapter on risk management contains both the basics as well as advanced topics, e. g. coherent risk measures, which have not yet reached the statistical physics community interested in ?nancial m- kets. Similarly, it is surprising how little research by academic physicists has appeared on topics relating to Basel II. Basel II is the new capital adequacy framework which will set the standards in risk management in many co- tries for the years to come. Basel II is responsible for many job openings in banks for which physicists are extemely well quali?ed. For these reasons, an outline of Basel II takes a major part of the chapter on capital. |

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### Contents

1 | |

Basic Information on Capital Markets | 13 |

Random Walks in Finance and Physics | 27 |

The BlackScholes Theory of Option Prices | 51 |

Scaling in Financial Data and in Physics 101 | 100 |

Turbulence and Foreign Exchange Markets | 173 |

Derivative Pricing Beyond BlackScholes | 197 |

Microscopic Market Models | 221 |

Theory of Stock Exchange Crashes 259 | 258 |

Risk Management | 289 |

Economic and Regulatory Capital | 325 |

Appendix | 359 |

367 | |

374 | |

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### Common terms and phrases

agents analysis assumed Bachelier Bachelier’s bank bank’s Basel Basel II behavior Black–Scholes bond call option correlations crash credit risk default defined depends derivative described diffusion discussed drift eigenvalues exchange expectation value exponent financial markets financial time series finite fluctuations future Gaussian distribution geometric Brownian motion hedging implied volatility important interest rate internal investment investors Lévy distribution Lévy flight limit log-periodic long position market risk martingale maturity multifractal operational risk option prices parameters payoff physics portfolio power law prediction price changes probability distribution put options Pvar random variables random walk real markets regulatory capital resp returns risk management risk measure risk-free riskless scale Sect shown in Fig simulation solid line Sornette stable Lévy distribution standard deviation statistical stochastic process stock market stock price strategy tails theory tion trading turbulence unexpected losses value at risk variance zero