Pricing Asian Options: A Comparison of Numerical and Simulation Approaches Twenty Years Later

Abstract

Abstract The calculation of the Asian option value has posed a great challenge to financial mathematicians as well as practitioners for the last two decades. Since there exists no analytical valuation formula to date, one has to resort to other methods to price this commonly used derivative product. One possibility is the usage of simulation approaches, which however are especially inefficient for Asian options, due to their dependence on the entire stock price trajectory. Another alternative is resorting to semi-analytical methods, based on the inversion of the option price’s Laplace transform, which however are prone to severe numerical difficulties. In this paper, we seek answer to the question whether it is possible to improve on the efficiency of the semi-analytical approach, implementing and comparing different numerical algorithms, so that they could be applied in real-life situations. We look into whether today’s superior computer environment has changed the relative strength of numerical and simulation approaches with regards to Asian option pricing. Based on a comprehensive analysis of speed and reliability, we find that the Laplace transform inversion method can be further enhanced, pushing down the prior critical value from 0.01 to 0.005 and the calculation time from 20 - 30 seconds to 3 - 4 seconds. This renders the numerical approach readily applicable for practitioners; however, we conclude that the simulation approach is a more efficient option when σ 2 <0.01.