Analytical binomial lookback options with double-exponential jumps

作者：Park Hyun Suk^*

来源：Journal of the Korean Statistical Society, 2009, 38(4): 397-404.

DOI：10.1016/j.jkss.2009.07.002

• Stochastic differential equation
• Adjusted binomial tree method
• Lookback option
• Exponential jumps
• Partial integro-differential equation
• Viscosity solution

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.

• 出版日期2009-12