ALTERNATIVE RANDOMIZATION FOR VALUING AMERICAN OPTIONS

This paper deals with randomization methods for valuing American options written on dividend-paying assets, which are based on the idea of treating the maturity date as a random variable. In the randomization method introduced by Carr in 1998, he used the Erlangian distributed random variable to develop a recursive algorithm starting from the so-called Canadian option with an exponentially distributed random maturity. The purposes of this paper are (i) to provide much simpler pricing formulas for the Canadian option; (ii) to interpret the Gaver-Stehfest method developed for inverting Laplace transforms as an alternative randomization method in the context of valuing American options; and (iii) to evaluate the performance of the Gaver-Stehfest method in details with theoretical and numerical views. Numerical experiments indicate that the Gaver-Stehfest method works well to generate accurate approximations for the early exercise boundary as well as the option value.