Objectives

In this course we intend to study and implement computationally algorithms for the numerical resolution of some problems in finance. We will study and implement the finite difference method to solve numerically differential equations and will study algorithms for the numerical resolution of obstacle problems (American options) and exotic (Asian) options.

 Program

1. Simulation of random variables
2. Monte Carlo and quasi-Monte Carlo methods
3. Finite difference method for parabolic equations
4. Numerical methods for stochastic differential equations
5. Numerical methods for obstacle problems (American options) and Asian options

Bibliography

• Achdou, Y. and Pironneau, O., Computational methods for option pricing, SIAM, 2005.
• Kloeden, P.E. and Platen, E., Numerical solution of stochastic differential equations, Springer, 1995.
• Seydel, R., Tools for Computational Finance, Springer, 2006.
• Wilmott, P., Dewynne, J. and Howison, S., Option pricing: Mathematical models and computation.