Valuation of Asian Options-with Levy Approximation

Abstract: Asian options are difficult to price analytically. Even though they have attracted much attention in recent years, there is still no closed-form solution available for pricing the arithmetic Asian options, because the distribution of the density function is unknown. However, various studies have attempted to solve this problem, Levy (1992) approximates the unknown density function using lognormal distribution by matching the first two moments. This paper investigates how accurate the Levy approach is by comparing values of Asian options from Levy’s approach with Monte Carlo simulations. We find that Levy’s analytic solution tends to over-estimate Asian option values when volatility is constant, but under-estimates under the scenario of having stochastic volatility.