AN EFFICIENT VARIANCE REDUCTION-BASED SIMULATION ALGORITHM FOR PRICING ARITHMETIC ASIAN OPTIONS

Abstract

This paper proposes a new hybrid algorithm to price the arithmetic Asian options under the geometric Brownian motion (GBM). The proposed algorithm is based on the control variate technique, such that the control variable is a combination of the barrier arithmetic Asian option and the geometric Asian option, which each one will be estimated by the importance sampling and the control variate techniques, respectively. Besides, we drive a conditional expectation for the estimator that it can reduce variance of simulations. The merits of the proposed algorithm for pricing arithmetic Asian options are illustrated by several examples.