The objective of this advanced-level course is to give the participants a good understanding of the Monte Carlo Method and its applications in finance. We shall start by motivating the use of Monte Carlo methods and we shall give an overview of the widespread use of Monte Carlo methods in securities and derivatives pricing and in risk management. We then give an in-depth explanation of the Monte Carlo method, enumerating its fundamental building blocks. We shall work our way through generation of pseudo-random numbers including numbers drawn from arbitrary probability distributions, discrete as well as continuous. We explain how the "Cholesky decomposition" technique can be used when sampling from multivariate distributions, when assets are correlated. We will use lattice-pricing models to price exotic options using various stochastic processes, including Black-Scholes as a benchmark. Further, we will show how to construct discrete versions of widely used Stochastic Differential Equations. These versions will be used to simulate trajectories of assets and to measure the Value at Risk of a portfolio of securities. Finally, we present quite a few variance reduction techniques for use with Monte Carlo Simulation, including the use of antithetic variables, control variates and importance sampling. The effect of these techniques on computational accuracy and/or performance will be evaluated. Throughout the course the participants will be given the opportunity to work on exercises, gaining hands-on experience with some of the Monte Carlo methods. (Excel and Visual Basic). The exercises/workshops will be based upon Microsoft Excel 2000 and Visual Basic.
