Approaches to Asian Option Pricing with Discrete Dividends

Abstract

The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian tail and those with monitoring throughout their lifespan is emphasized. Rates of convergence are confirmed, but greater focus is put on actual performance in regions of accuracy which are realistic for use by practitioners. A hybrid approach combining Curran's analytical approximation with a two-dimensional finite difference method is examined with respect to the errors caused by the approximating assumptions. For Asian tails of equidistant monitoring dates, this method performs very well, but as the scenario deviates from the method's ideal conditions, the errors in the approximation grow unfeasible. For general monitoring straightforward solution of the full three-dimensional partial differential equation by finite differences is highly accurate but suffers from rapid degradation in performance as the monitoring interval increases. For options with long monitoring intervals a randomized quasi-Monte Carlo method with control variate variance reduction stands out as a powerful alternative.