9783540929284

3540929282

Universitext

Modeling tools for financial options. Options ; model of the financial market ; Numerical methods ; The binomial method ; Risk-Neutral valuation ; Stochastic process ; Diffusion models ; Itô Lemma and applications ; Jump models ; Calibration ; Notes and comments ; Exercises

Generating random numbers with specified distributions. Uniform deviates ; Extending to random variables from other distributions ; Normally distributed random variables ; Monte Carlo integration ; Sequence of numbers with low discrepancy ; Notes and comments ; Exercises

Monte Carlo simulation with stochastic differential equations. Approximation error ; Stochastic Taylor expansion ; Examples of numerical methods ; Intermediate values ; Monte Carlo simulation ; Monte Carlo methods for American options ; Notes and comments ; Exercises

Standard methods for standard options. preparations ; Foundations of finite-difference methods ; Crank-Nicolson method ; Boundary conditions ; American options as free boundary problems ; Computation of American options ; On the accuracy ; Analytic methods ; Notes and comments ; Exercises

Finite-element methods. Weighted residuals ; Galerkin approach with hat functions ; Application to standard options ; Application to an exotic call option ; Error estimates ; Notes and comments ; Exercises

Pricing of exotic options. Exotic options ; Options depending on several assets ; Asian options ; Numerical aspects ; Upwind schemes and other methods ; High-resolution methods ; Notes and comments ; Exercises

Appendices. Financial derivatives ; Stochastic tools ; Numerical methods ; Complementary material.

Finance > Mathematical models.

Finance > Mathematical models.