Pricing of American Call Options

Consider an American basket call option on two assets of which the vector (S1(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.