Monte Carlo Simulation

Abstract

This chapter explains the principles of Monte Carlo integration techniques, a class of computational algorithms, and their applications for the pricing of derivatives. It discusses the different discretization techniques for the stochastic differential equations used to model the propagation of the underlying risk factors. The Libor market model (LMM) is examined as an example of a high-dimensional model where Monte Carlo methods are typically applied to valuate derivatives. The chapter emphasizes on random number generation, which is one of the major building blocks of every Monte Carlo-based pricing routine. There is a vast amount of literature covering uniform and nonuniform random variate generation in detail. A short overview of the most important methods is presented.

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