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

• Published in: Journal of mathematical analysis and applications Vol. 330; no. 1; pp. 10 - 23
• Main Authors: Kim, Kwang Ik, Qian, Xiao-song
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.06.2007; Elsevier
• Subjects: Applications; Asian option; Binomial tree method; Exact sciences and technology; Insurance, economics, finance; Jump-diffusion model; Mathematical analysis; Mathematics; Partial differential equations; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic analysis; Viscosity solution; Jump-diffusion model; Binomial tree method; Asian option; Viscosity solution; Uniform convergence; Difference scheme; Finance; American option; Numerical analysis; Equivalence; Mathematical analysis; Jump diffusion; Pricing; Discrete time; Financial option
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2006.07.042

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.