The Prcing of American Put Options and Numerical Solution Based on Approximating Hedge Jump Risk

Operations Research and Management Science ›› 2014, Vol. 23 ›› Issue (3): 226-233.

Previous Articles Next Articles

The Prcing of American Put Options and Numerical Solution Based on Approximating Hedge Jump Risk

YUAN Guo-jun, XIAO Qing-xian

Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2012-03-23 Online:2014-03-25

基于近似对冲跳跃风险的美式看跌期权定价及数值解法研究

袁国军, 肖庆宪

上海理工大学管理学院,上海 200093

作者简介:袁国军(1981-),男,安徽霍邱人,博士研究生,副教授,研究方向:金融工程,金融数学;肖庆宪(1956-),男,河南信阳人,博士,教授,博士生导师,研究方向:金融工程,金融数学。
基金资助:
国家自然科学基金资助项目(11171221);上海市一流学科(系统科学)资助项目(XTKX2012)

Abstract

Abstract: In this paper, the pricing for American put option is considered based on approximating hedge jump risk. Firstly, the options pricing model and the partial differential equation of the options pricing model are derived in the jump-diffusion process, by applying the generalized It formula and no-arbitrage principle, based on approximating hedge jump risk. The approximate implicit difference scheme of American put option pricing model is developed, and consistency, well-posedness, stability and convergence of the difference scheme are also proved in this paper. Lastly, the numerical experiments show that this method is an effective and feasible way for pricing American options in jump-diffusion model.

Key words: option pricing, american options, numerical method, stability analysis, convergence analysis

摘要： 考虑了基于近似对冲跳跃风险的美式看跌期权定价问题。首先,运用近似对冲跳跃风险、广义It 公式及无套利原理,得到了跳-扩散过程下的期权定价模型及期权价格所满足的偏微分方程。然后建立了美式看跌期权定价模型的隐式差分近似格式,并且证明了该差分格式具有的相容性、适定性、稳定性和收敛性。最后,数值实验表明,用本文方法为跳-扩散模型中的美式期权定价是可行的和有效的。

关键词: 期权定价, 美式期权, 数值方法, 稳定性分析, 收敛性分析

CLC Number:

F830.9

YUAN Guo-jun, XIAO Qing-xian. The Prcing of American Put Options and Numerical Solution Based on Approximating Hedge Jump Risk[J]. Operations Research and Management Science, 2014, 23(3): 226-233.

袁国军, 肖庆宪. 基于近似对冲跳跃风险的美式看跌期权定价及数值解法研究[J]. 运筹与管理, 2014, 23(3): 226-233.

References

[1] Black F, Scholes M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81(3): 637-655.
[2] Kou S G. A Jump-diffusion model for option pricing[J]. Management Science, 2002, 48(8): 1086-1101.
[3] Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1-2): 125-144.
[4] Jarrow R A, Rosenfeld E R. Jump risks and the intertemporal capital asset pricing model[J]. Journal of Business, 1984, 57(3): 337-351.
[5] Cox J C, Ross S A. The pricing of options for jump processes[J]. University of Pennsylvania: Rodney L. White Center Working Paper, 1975. 2-75.
[6] Bardhan I, Chao X. Martingale analysis for assets with discontinuous returns[J]. Mathematics of Operations Research, 1995, 20(1): 243-256.
[7] Aase K K. Contingent claim valuation when the security price is a combination of an Ito process and a random point process[J]. Stochastic Processes and their Applications, 1988, 28(2): 185-220.
[8] Scott L O. Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: applications of Fourier inversion method[J]. Mathematical Finance, 1997,7(4): 413-426.
[9] Gukhal C R. Analytical valuation of american options on jump-diffusion processes[J]. Mathematical Finance, 2001, 11(1): 97-115.
[10] Chockalingam A, Muthuraman K. Pricing american options when assets prices jump[J]. Operation Research Letters, 2010, 38(2): 82-86.
[11] 范玉莲,孙志宾.跳跃-扩散模型中期权定价的倒向随机微分方程方法及等价概率鞅测度[J].应用数学学报,2009,32(4):673-681.
[12] 王春发,王翠萍.基于FFT的区域变换对数均匀跳扩散模型期权定价[J].运筹与管理,2011,20(2):152-159.
[13] 姜礼尚,罗俊.跳-扩散模型下永久美式看跌期权定价[J].系统工程理论与实践,2008,(2):10-18.
[14] 邓国和,黄艳华.双指数跳扩散模型的美式二值期权定价[J].高校应用数学学报,2011,26(1):21-26.
[15] 邓国和,杨向群.随机波动率与双指数跳-扩散组合模型的美式期权定价[J].应用数学学报,2009,32(2):236-255.
[16] Salmi S, Toivanen J. An iterative method for pricing american options under jump-diffusion models[J]. Applied Numerical Mathematics, 2011, 61(7): 821-831.
[17] Cont R, Tankov P. Financial modeling with jump process[M]. Boca Raton: Chapman and Hall/CRC, 2004.
[18] 许友才,胡兵.美式看跌期权定价问题的修正C-N格式求解[J].高校计算数学学报,2009,31(1):70-76.
[19] 张铁,祝丹梅.美式期权定价问题的变网格差分方法[J].计算数学,2008,30(4):379-387.
[20] Kou S G, Wang H. Option pricing under a double exponential jump diffusion model[J]. Management Science, 2004, 50(9): 1178-1192.
[21] Amin K. Jump diffusion option valuation in discrete time[J]. J. Finance,1993, 48(5): 1833-1863.
[22] Balaban E. Comparative forecasting performance of symmetric and asymmetric conditional volatility modek of an exchange rate[J]. Economics Letters, 2004, 83(1): 99-105.

The Prcing of American Put Options and Numerical Solution Based on Approximating Hedge Jump Risk

基于近似对冲跳跃风险的美式看跌期权定价及数值解法研究

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 7

Recommended Articles

Metrics

[1]	LIU Gui-fang, XU Wei-jun, HUANG Jing-long, ZHAO Qi. European Vulnerable Option Pricing Considering Corporate Information Disclosure Emotion [J]. Operations Research and Management Science, 2021, 30(9): 164-171.
[2]	LEI Ming, CHEN Shu-xin, YE Wu-yi. A Comparative Study of Option Pricing Models: Based on Bilateral Gamma Distribution Model and B-S Model [J]. Operations Research and Management Science, 2021, 30(7): 190-194.
[3]	LI Ming-xin, TANG Jun, BAI Yun, MA Xing-da. Screw Thread Steel Option Pricing Based on Optimized Black-Scholes Model [J]. Operations Research and Management Science, 2019, 28(10): 117-122.
[4]	HU Rong, ZHENG Jun. The Pricing Model of Housing Presale Contract in Option Perspective [J]. Operations Research and Management Science, 2017, 26(11): 154-160.
[5]	ZHANG Gao-xun, ZHANG Hong-lei. Option Pricing Model Based on Asymmetric GARCH-GH and Its Empirical Analysis [J]. Operations Research and Management Science, 2017, 26(11): 161-168.
[6]	HUANG Xing, WANG Shao-yu. Research on Emergency Material Reserve Strategies Based on Stability Analysis [J]. Operations Research and Management Science, 2014, 23(1): 15-19.
[7]	WANG Chun-fa, WANG Cui-ping. Option Pricing for a Jump Diffusion Model with Log-Uniform Jump-Amplitudes in a Regime-Switching Market Using FFT [J]. Operations Research and Management Science, 2011, 20(2): 152-159.