The Statistical Mechanics of Financial Markets

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Springer Science & Business Media, Apr 17, 2013 - Mathematics - 290 pages

"Provides an excellent introduction for physicists interested in the statistical properties of financial markets... basic financial terms such as shorts, limit orders, puts, calls, and other terms are clearly defined... an excellent starting point for the interested physicist." PHYSICS TODAY
This introductory treatment describes parallels between statistical physics and finance, both long established and new research results on capital markets. Forming the core of Voit's treatment are the concepts of random walks, scaling of data, and risk control. Voit discusses the underlying assumptions using empirical financial data and analogies to physical models such as fluid flows and turbulence. He formulates theories of derivative pricing and risk control, and shows how computer simulations of markets provide insights into price fluctuations and how crashes are modelled in ways analogous to phase transitions. This corrected edition has been updated with several new and significant developments, e.g. the dynamics of volatility smiles and implied volatility surfaces, path integral approaches to option pricing, a new simulation scheme for options, multifractals, the application of nonextensive statistical mechanics to financial markets, and the minority game.

 

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Contents

Introduction
1
Basic Information on Capital Markets
13
Random Walks in Finance and Physics
25
The BlackScholes Theory of Option Prices
49
Scaling in Financial Data and in Physics
85
Turbulence and Foreign Exchange Markets
153
Risk Control and Derivative Pricing
177
Microscopic Market Models 209
208
Theory of Stock Exchange Crashes
247
Information Sources
271
Index
285
Copyright

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