Conditional Moment Matching for Pricing Arithmetic Asian Options under Vasicek Interest Rate Model*

Under the Vasicek interest rate model, a conditional moment matching approximation for pricing arithmetic Asian options is introduced in this paper. The essential idea of this approximation is to find a proper gamma or lognormal distribution by conditional moment matching to approximate the conditional distribution of the underlying asset's integral given the terminal value of the underlying asset. In order to deal with the two-dimensional stochastic models with Vasicek interest rate, a change of measure techniques is applied to separate the stochastic interest rate and the underlying asset in the expectation about the present value of Asian option's payoff function, thus it allows to apply the stratified approximation to the conditional distribution of the integral of the underlying asset. Based on the benchmark price of Asian options by Monte Carlo simulation, we test the efficiency and robustness of the proposed approximation method by some numerical examples. It is found that this approximation method improves greatly in computation speed over standard Monte Carlo simulation while keeping precision of the price, and the approximation by lognormal distribution is more accurate than by gamma distribution in general.