Theory of financial risk and derivative pricing: from statistical physics to risk management (2nd ed)

Risk control and derivative pricing are major concerns to financial institutions. The need for adequate statistical tools to measure and anticipate amplitude of potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are based on assumptions leading to systematic (sometimes dramatic) underestimation of risks. Theory of financial risk and derivative pricing summarises developments, some inspired by statistical physics, using which one can take into account more faithfully the real behaviour of financial markets for asset allocation, derivative pricing and hedging, and risk control.

Contents:

• Probability theory: basic notations, Maximum and addition of random variables, Continuous time limit, Ito calculus and path integrals, Analysis of empirical data, Financial products and financial markets
• Statistics of real prices: basic results, Non-linear correlations and volatility fluctuation, Skewness and price-volatility correlations, Cross-correlations, Risk measures, Extreme correlations and variety, Optimal portfolios
• Futures and options: fundamental concepts
• Options: hedging and residual risk
• Options: the role of drift and correlations
• Options: the Black and Scholes model
• Options: some more specific problem
• Options: minimum variance Monte Carlo, The yield curve, Simple mechanisms for anomalous price statistics.