Convergence of the binomial tree method for Asian options in jump-diffusion models |
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Authors: | Kwang Ik Kim |
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Institution: | a Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea b School of Mathematical Science, Yangzhou University, Yangzhou 225002, PR China |
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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. |
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Keywords: | Binomial tree method Asian option Jump-diffusion model Viscosity solution |
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