New control variates for pricing basket and Asian options

Abstract

In this thesis, we investigate new control variates for simulation-based pricing of options where the option price is a function of the sum of (or integral of) lognormal random variables. We use two different approaches: one is the use of Hermite polynomial approximation of the relevant function and another is the use of upper and lower bounds on the option prices obtained using the properties of Brownian motion. We provide detailed numerical experiments to illustrate the use of these approaches for accurate and low variance pricing basket and Asian options. First order Hermite polynomial approximation also gives a reasonable direct approximation to the basket or Asian option price for at the money and in-the-money options.