Introduction |
Discrete-time models / 1: |
Discrete-time formalism / 1.1: |
Martingales and arbitrage opportunities / 1.2: |
Complete markets and option pricing / 1.3: |
Problem: Cox, Ross and Rubinstein model / 1.4: |
Exercises / 1.5: |
Optimal stopping problem and American options / 2: |
Stopping time / 2.1: |
The Snell envelope / 2.2: |
Decomposition of supermartingales / 2.3: |
Snell envelope and Markov chains / 2.4: |
Application to American options / 2.5: |
Brownian motion and stochastic differential equations / 2.6: |
General comments on continuous-time processes / 3.1: |
Brownian motion / 3.2: |
Continuous-time martingales / 3.3: |
Stochastic integral and Ito calculus / 3.4: |
Stochastic differential equations / 3.5: |
The Black-Scholes model / 3.6: |
Description of the model / 4.1: |
Change of probability. Representation of martingales / 4.2: |
Pricing and hedging options in the Black-Scholes model / 4.3: |
American options / 4.4: |
Implied volatility and local volatility models / 4.5: |
The Black-Scholes model with dividends and call/put symmetry / 4.6: |
Problems / 4.7: |
Option pricing and partial differential equations / 5: |
European option pricing and diffusions / 5.1: |
Solving parabolic equations numerically / 5.2: |
Interest rate models / 5.3: |
Modelling principles / 6.1: |
Some classical models / 6.2: |
Asset models with jumps / 6.3: |
Poisson process / 7.1: |
Dynamics of the risky asset / 7.2: |
Martingales in a jump-diffusion model / 7.3: |
Pricing options in a jump-diffusion model / 7.4: |
Credit risk models / 7.5: |
Structural models / 8.1: |
Intensity-based models / 8.2: |
Copulas / 8.3: |
Simulation and algorithms for financial models / 8.4: |
Simulation and financial models / 9.1: |
Introduction to variance reduction methods / 9.2: |
Computer experiments / 9.3: |
Appendix |
Normal random variables / A.1: |
Conditional expectation / A.2: |
Separation of convex sets / A.3: |
Bibliography |
Index |
Introduction |
Discrete-time models / 1: |
Discrete-time formalism / 1.1: |