Convergence of the binomial tree method for Asian options in jump-diffusion models

Abstract

The binomial tree methods (BTM), first proposed by Cox, Ross and Rubinstein [J. Cox, S. Ross, M. Rubinstein, Option pricing: A simplified approach, J. Finan. Econ. 7 (1979) 229–264] in diffusion models and extended by Amin [K.I. Amin, Jump diffusion option valuation in discrete time, J. Finance 48 (1993) 1833–1863] to jump-diffusion models, is one of the most popular approaches to pricing options. In this paper, we present a binomial tree method for Asian options in jump-diffusion models and show its equivalence to certain explicit difference scheme. Employing numerical analysis and the notion of viscosity solution, we prove the uniform convergence of the binomial tree method for European-style and American-style Asian options.