JAMP  Vol.7 No.12 , December 2019
A New Binomial Tree Method for European Options under the Jump Diffusion Model
Abstract: In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.
Cite this paper: Zhu, L. , Kan, X. , Shu, H. and Wang, Z. (2019) A New Binomial Tree Method for European Options under the Jump Diffusion Model. Journal of Applied Mathematics and Physics, 7, 3012-3021. doi: 10.4236/jamp.2019.712211.

[1]   Cox, J.C. and Ross, S.A. (1976) The Valuation of Options for Alternative Stochastic Process. Journal of Financial Economics, 3, 145-166.

[2]   Merton, R.C. (1976) Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3, 125-144.

[3]   Kou, S.G. (2002) A Jump-Diffusion Model for Option Pricing. Management Science, 48, 1086-1101.

[4]   Boyarchenko, O. and Levendorskii, S. (2005) American Option: The EPV Pricing Model. Annals of Finance, 1, 267-292.

[5]   Cox, J.C., Ross, S.A. and Rubinstein, M. (1979) Option Pricing: A Simplified Approach. Journal of Financial Economics, 7, 229-263.

[6]   Amin, K. (1993) Jump Diffusion: Option Valuation in Discrete Time. Journal of Finance, 48, 1833-1863.

[7]   Alfredo, I. and Fernando, Z. (2004) Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier. Journal of Financial & Quantitative Analysis, 39, 253-275.

[8]   Shi, G. and Zhou, S. (2012) The Binomial Tree Method for European Option Mathematical Theory and Applications. Mathematical Theory and Applications, 32, 19-26. (In Chinese)

[9]   Zhang, H. and Yue, Y. (2006) No-Arbitrage Conditions of Binary Tree Option Pricing. Economic Mathematics, No. 4, 34-37.

[10]   Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 635-654.

[11]   Hull, J. and White, A. (1990) Pricing Interest Rate Derivative Securities. Review of Financial Studies, 3, 573-592.

[12]   Xu, W. and Wu, C. (2009) A Jump-Diffusion Model for Option Pricing under Fuzzy Environments. Mathematics and Economics, 44, 337-344.

[13]   Sudaa, S. and Muroi, Y. (2015) Computation of Greeks Using Binomial Trees in a Jump-Diffusion Model. Journal of Economic Dynamics Control, 51, 93-110.

[14]   Cheng, L., Xiao, S. and Li, S. (2003) Numerical Analysis on Binomial Tree Methods for a Jump-Diffusion Model. Journal of Computational and Applied Mathematics, 156, 23-45.

[15]   Liu, J., Wu, W., Xu, J. and Zhao, H. (2014) An Accurate Binomial Model for Pricing American Asian Option. Journal of System Science and Complexity, 27, 993-1007.

[16]   Jiang, Y., Song, S. and Wang, Y. (2018) Pricing European Vanilla Options under a Jump-to-Default Threshold Diffusion Model. Journal of Computational and Applied Mathematics, 344, 438-456.

[17]   Lian, Y. (2010) Application of a New Type of Binomial Parameter Model for Asian Options Pricing. Journal of Henan Normal University (Natural Science), 38, 28-30. (In Chinese)

[18]   Zhang, T. (2000) A New Option Pricing Binomial Tree Parameter Model. Systems Engineering and Theory Practice, 11, 90-93. (In Chinese)