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

The derivation of Asian option value has posed a challenge to financial mathematicians for the last two decades. Fu, Madan and Wang (1999) made a comparison between the Laplace transform approach and the Monte Carlo approach, and found that the numerical inversion method encountered severe numerical instabilities when volatility was low or maturity was short.In this paper, we seek to answer the question whether it is possible to improve on the efficiency of the inversion, implementing and comparing different numerical algorithms, so that the Laplace transform could be used in real-life situations. We also 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 an detailed comparison of methods, we find that the speed and reliability of the Laplace transform inversion could be further enhanced, pushing down the prior critical value from 0.01 to 0.005 and calculation time from 20-30 seconds to 3-4 seconds. Also, as a conclusion of our research we suggest that the simulation approach be used when sigma^2*T < 0.01