The Statistical Mechanics of Financial Markets (Theoretical and Mathematical Physics)

This highly praised introductory treatment describes the parallels between statistical physics and finance - both those established in the 100-year long interaction between these disciplines, as well as new research results on financial markets. The random-walk technique, well known in physics, is also the basic model in finance, upon which are built, for example, the Black-Scholes theory of option pricing and hedging, plus methods of portfolio optimization. Here the underlying assumptions are assessed critically. Using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion, the book develops a more accurate description of financial markets based on random walks. With this approach, novel methods for derivative pricing and risk management can be formulated. Computer simulations of interacting-agent models provide insight into the mechanisms underlying unconventional price dynamics. It is shown that stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes, and sometimes have even been predicted successfully. This third edition of "The Statistical Mechanics of Financial Markets" especially stands apart from other treatments because it offers new chapters containing a practitioner's treatment of two important current topics in banking: the basic notions and tools of risk management and capital requirements for financial institutions, including an overview of the new Basel II capital framework which may well set the risk management standards in scores of countries for years to come. From the reviews - "Provides an excellent introduction for physicists interested in the statistical properties of financial markets. Appropriately early in the book the basic financial terms such as shorts, limit orders, puts, calls, and other terms are clearly defined. Examples, often with graphs, augment the reader’s understanding of what may be a plethora of new terms and ideas... [This is] an excellent starting point for the physicist interested in the subject. Some of the book’s strongest features are its careful definitions, it detailed examples, and the connection it establishes to physical systems." PHYSICS TODAY, August 2002 "This book is excellent at illustrating the similarities of financial markets with other non-equilibrium physical systems. [...] In summary, a very good book that offers more than just qualitative comparisons of physics and finance." (www.quantnotes.com) This textbook describes parallels between statistical physics and finance - both those established in the 100-year-long interaction between these disciplines, as well as new research results on capital markets. The random walk, well known in physics, is also the basic model in finance, upon which are built, for example, the Black-Scholes theory of option pricing and hedging, or methods of risk control using diversification. Here the underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated. Computer simulations of interacting agent models of financial markets provide insights into the origins of asset price fluctuations. Stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes. These models allow for predictions. This study edition has been updated with a presentation of several new and significant developments, e.g. the dynamics of volatility smiles and implied volatility surfaces, path integral approaches to option pricing, a new and accurate simulation scheme for options, multifractals, the application of nonextensive statistical mechanics to financial markets, and the minority game. The 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. This Third Edition Includes Two New Chapters Containing A Practitioner's Treatment Of Two Important Current Topics In Banking: The Basic Notions And Tools Of Risk Management And Capital Requirements For Financial Institutions, Including An Overview Of The New Basel Ii Capital Framework. 1. Introduction -- 2. Basic Information On Capital Markets -- 3. Random Walks In Finance And Physics -- 4. The Black-scholes Theory Of Option Prices -- 5. Scaling In Financial Data And In Physics -- 6. Turbulence And Foreign Exchange Markets -- 7. Derivative Pricing Beyond Black-scholes -- 8. Microscopic Market Models -- 9. Theory Of Stock Exchange Crashes -- 10. Risk Management -- 11. Economic And Regulatory Capital For Financial Institutions -- Appendix. Johannes Voit. Information Sources: P. [359]-363. Includes Bibliographical References (p. [365]-393) And Index. Introduction....Pages 1-11 Basic Information on Capital Markets....Pages 13-25 Random Walks in Finance and Physics....Pages 27-50 The Black-Scholes Theory of Option Prices....Pages 51-99 Scaling in Financial Data and in Physics....Pages 101-172 Turbulence and Foreign Exchange Markets....Pages 173-196 Derivative Pricing Beyond Black—Scholes....Pages 197-219 Microscopic Market Models....Pages 221-257 Theory of Stock Exchange Crashes....Pages 259-288 Risk Management....Pages 289-324 Economic and Regulatory Capital for Financial Institutions....Pages 325-358 "This third edition of The Statistical Mechanics of Financial Markets especially stands apart from other treatments because it offers new chapters containing a practitioner's treatment of two important current topics in banking: the basic notions and tools of risk management and capital requirements for financial institutions, including an overview of the new Basel II capital framework which may well set the risk management standards in scores of countries for years to come."--Résumé de l'éditeur "This third edition of The Statistical Mechanics of Financial Markets especially stands apart from other treatments because it offers new chapters containing a practitioner's treatment of two important current topics in banking: the basic notions and tools of risk management and capital requirements for financial institutions, including an overview of the new Basel II capital framework which may well set the risk management standards in scores of countries for years to come."--Jacket Offers chapters on the basic notions and tools of risk management, and capital requirements for financial institutions. Using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion, this book develops a description of financial markets based on random walks