Analytical binomial lookback options with double-exponential jumps

• Published in: Journal of the Korean Statistical Society Vol. 38; no. 4; pp. 397 - 404
• Main Author: Park, Hyun Suk
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.12.2009; Springer Singapore; 한국통계학회
• Subjects: Adjusted binomial tree method; Applied Statistics; Bayesian Inference; Exponential jumps; Lookback option; Partial integro-differential equation; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Stochastic differential equation; Viscosity solution; 통계학; 65C20; 60H30; Partial integro-differential equation; Viscosity solution; Exponential jumps; Adjusted binomial tree method; 62P05; 91B28; Lookback option; Stochastic differential equation
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2009.07.002

We study the problem of the convergence of the adjusted binomial lookback option in double-exponential jump diffusion models. By using the results of [Dai, M., (2000). A modified binomial tree method for currency lookback options. Acta Mathematica Sinica, 16, 445–454; Kou, S., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192] and [Park, H.S., Kim, K.I., & Qian, X. (2009). A Mathematical modeling for the Lookback option with jump diffusion using Binomial tree method. Journal of Computational and Applied Mathematics, preprint], we show the equivalence between the adjusted binomial tree method and the explicit difference scheme. The convergence is also theoretically proved through the notion of viscosity solution. Numerical results coincide with the theoretical results.