Synopsis for Numerical Methods 2: Monte Carlo Methods

Monte Carlo estimation, Central Limit Theorem, condence intervals; generation of random and quasi-random numbers; variance reduction and the estimation of Greeks.
Euler-Maruyama and Milstein approximations of SDEs; weak and strong convergence and numerical analysis; quasi-Monte Carlo with Brownian Bridge and PCA constructions; mul- tilevel approach; Longsta-Schwarz method for Bermudan and American options.

This course gives a comprehensive introduction to Monte-Carlo methods for pricing nancial options, and evaluating their sensitivities to various input parameters. The rst third of the course looks at methods for cases in which the payo depends on the nal state and this can be directly simulated.
The remainder of the course considers path-dependent cases in which the complete solution to the underlying stochastic dierential equation must be simulated.
At the end of the course, the student should have a thorough understanding of the theory behind Monte Carlo methods, be able to implement them for a range of applications, and have an appreciation of some of the current research areas.

The primary text for the course is;

1. P Glasserman, Monte Carlo Methods in Financial Engineering, Springer-Verlag, 2004.
2. P.E Kloeden, E Platen Numerical Solutions of Stochastic Differential Equations, Springer Verlag, 1992.
3. S. Asmussen, P. Glynn, Stochastic Simulation: Algorithms and Analysis, Springer, 2007 (or 2010)