Single-Transform Formulas for Pricing Asian Options in a General Approximation Framework under Markov Processes

Abstract

Recently, Cai et al. (2015) proposed closed-form double transform approxima- tion formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z−transform and the Laplace transform involved in their final results, respectively, for the discretely and the con- tinuously monitored cases, and we obtain explicit single Laplace transforms of option prices. This reduction in the dimension of numerical integral has meaningful consequences both in computational efficiency and in practical implementation of the formulas. Extensive numerical experiments illustrate the improved performance of our results.

Keywords: Finance, Asian option, Markov process, Continuous-Time Markov Chain, Laplace transform

JEL Classification: G12, G13