Risk control and derivative pricing have become of major concern to financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are based on simplified assumptions and lead to a systematic (and sometimes dramatic) underestimation of real risks. Theory of Financial Risk and Derivative Pricing summarises recent theoretical developments, some of which were inspired by statistical physics. Starting from the detailed analysis of market data, one can take into account more faithfully the real behaviour of financial markets (in particular the 'rare events') for asset allocation, derivative pricing and hedging, and risk control. INDICE 1. Probability theory: basic notions 2. Maximum and addition of random variables 3. Continuous time limit, Ito calculus and path integrals 4. Analysis of empirical data 5. Financial products and financial markets 6. Statistics of real prices: basic results 7. Non-linear correlations and volatility fluctuation 8. Skewness and price-volatility correlations 9. Cross-correlations 10. Risk measures 11. Extreme correlations and variety 12. Optimal portfolios 13. Futures and options: fundamental concepts 14. Options: hedging and residual risk 15. Options: the role of drift and correlations 16. Options: the Black and Scholes model 17. Options: some more specific problems 18. Options: minimum variance Monte Carlo 19. The yield curve 20. Simple mechanisms for anomalous price statistics