The objective of this advanced-level course is to give the participants hands-on experience with the use of advanced simulation techniques in finance. We start with an introduction to the Monte Carlo method and we 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. Participants will work their way through the generation of pseudo-random numbers including numbers drawn from arbitrary probability distributions, discrete as well as continuous. Participants will also learn and try how the "Cholesky decomposition" technique can be used when sampling from multivariate distributions, when assets are correlated. We use lattice-pricing to price and risk assess exotic options such as Asian, barrier and lookback options using various stochastic processes, including Black-Scholes as a benchmark. Further, we show how to construct discrete versions of widely used Stochastic Differential Equations. Participants will use these to simulate trajectories of assets and to measure the Value at Risk of a portfolio of securities, estimate the potential exposure of market driven instruments etc., and to perform "stress testing". Finally, we present a number of variance reduction techniques for use with Monte Carlo Simulation, including the use of antithetic variables, control variate and importance sampling methods. 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™).
