Novel Importance Sampling for the Valuation of Basket and Asian Options

Abstract

In this paper we discuss the use of a new method of importance sampling in the pricing of European options on a basket of assets and on average price (Asian) options. In standard Monte Carlo estimation the expectation is taken with respect to a vector which is distributed as n variate normal, where n is the number of assets in the basket, or the number of points in the averaging computation in the case of an Asian option. A change of measure which results in sampling the ratio of arithmetic to geometric average payoffs is central to the importance sampling method employed. Since this ratio varies little, considerable variance reduction can be achieved, particularly when the call option is 'in the money'. Experimental results are given.