Pricing Asian Options: a Comparison of Analytical and Monte Carlo Methods

Asian options paying the excess over strike, of either the arithmetic or geometric average of the asset price over either discrete or continuous time, are valued using analytical and simulation methodologies. Expressions are developed for the double Laplace transform of the continuous arithmetic Asian option in both its strike and maturity. Analytical option prices for the continuous arithmetic case are obtained by inverting the Geman and Yor (1993) Laplace transform in maturity using implementations of the Eu-ler and Post-Widder methods developed by Abate and Whitt (1995). Our results show that for continuous-time, path-dependent options, naive simulation can be expensive, in-eecient and inaccurate with 16% pricing errors. In addition to improving the precision of the simulation estimates by the judicious device of control variates, our experiments indicate that a reduction in bias requires the use of independently seeded replications and random number generators with much longer periods. Lastly, we observe that for pricing continuous-time contracts, there is an advantage to using suitably biased control variates that correct for the discretization bias inherent in simulation.