Bouchaud Jean-Philippe, Potters Marc. Theory of Financial Risks: From Statistical Physics to Risk Management

Cambridge: University Press, 2001. — 234 p. — ISBN: 0-521-78232-5.This book summarizes recent theoretical developments inspired by statistical physics in the description of the potential moves in financial markets, and its application to derivative pricing and risk control. The possibility of accessing and processing huge quantities of data on financial markets opens the path to new methodologies where systematic comparison between theories and real data not only becomes possible, but mandatory. This book takes a, physicist's point of view of financial risk by comparing theory with experiment. Starting with important results in probability theory the authors discuss the statistical analysis of real data, the empirical-determination of statistical laws, the definition of risk, the theory of optimal portfolio and the problem of derivatives (forward contracts, options). This book will be of interest to physicists interested in finance, quantitative analysts in financial institutions, risk managers and graduate students in mathematical finance.Probability theory: basic notions.Probabilities.
Some useful distributions.
Maximum of random variables - statistics of extremes.
Sums of random variables.
Central limit theorem.
Correlations, dependence, non-stationary models.
Central limit theorem for random matrices.
Appendix A: non-stationarity and anomalous kurtosis.
Appendix B: density of eigenvalues for random correlation matrices.
Statistics of real prices.
Aim of the chapter.
Second-order statistics.
Temporal evolution of fluctuations.
Anomalous kurtosis and scale fluctuations.
Volatile markets and volatility markets.
Statistical analysis of the forward rate curve.
Correlation matrices.
A simple mechanism for anomalous price statistics.
A simple mode] with volatility correlations and tails.Extreme risks and optimal portfolios.
Risk measurement and diversification.
Portfolios of uncorrelated assets.
Portfolios of correlated assets.
Optimized trading.
Conclusion of the chapter.
Appendix C: some useful results.
Futures and options: fundamental concepts.Futures and forwards.
Options: definition and valuation.
Optimal strategy and residual risk.
Does the price of an option depend on the mean return?
Conclusion of the chapter: the pitfalls of zero-risk.
Appendix D: computation of the conditional mean.
Appendix E: binomial model.
Appendix F: option price for (suboptimal) zl-hedging.
Options: some more specific problems.
Other elements of the balance sheet.
Other types of options: 'Puts' and 'exotic options'.
The 'Greeks' and risk control.
Value-at-risk for general non-linear portfolios.
Risk diversification.
Short glossary of financial terms.