Advanced Monte Carlo simulations and option pricing.

摘要

Consider the problem of pricing options whose payoffs depend on multiple sources of risk (rainbow options). Generally, under well known risk neutrality assumptions, the prices of options are calculated to be the expected value of future cash flows, discounted with the appropriate risk-free interest rate. However, for many rainbow options, the derivation of close-form solutions do not exist. Therefore, there is a need to rely on numerical methods such as lattice and finite difference methods or Monte Carlo simulation.; This thesis deals with the use of Monte Carlo simulation of stochastic processes as applied to option pricing. We numerically develop higher order discretization methods for stochastic differential equations and compare their accuracy for high dimensional option pricing problems. Furthermore, a new quasi-random variance reduction technique, extending classical antithetic variates, is introduced to increase simulation efficiency. This is applied to rainbow options, up to 100 assets, and underlyings with stochastic volatility.