Pricing of American Call Options

Consider an American basket call option on two assets of which the vector (S_t(t) , S₂(t)) of asset prices at time t follows a two-dimensional Levy process. Pricing the American call option will entail calculating the expected discounted value of its payoff. Presently, we introduce a method based on numerical integration for pricing two-dimensional American options where there is a finite, but possibly large, number of exercise dates. The results thus obtained show that the non-normality feature in the Levy process does have an effect on the prices of the American call options.

I. Introduction

A major characteristic of the American options is that they can be exercised prior to the maturity date. Pricing of American options is known to be a difficult problem especially when the number of underlying assets is large. Methods for pricing of an American option include Monte Carlo simulation, regression approach (See Tsitsiklis and Van Roy (1999) and Longstaff and Schwartz (2001)) and stochastic mesh method (See Broadie and Glasserman (1997),Avramidis and Hyden (1999), Avramidis and Matzinger (2004), Liu G and Hong L.J (2008)).