在跳环境和混合高斯过程下的资产定价及模拟

doi:10.6040/j.issn.1671-9352.0.2019.666

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (5): 105-113.doi: 10.6040/j.issn.1671-9352.0.2019.666

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在跳环境和混合高斯过程下的资产定价及模拟

彭波,郭精军^*

兰州财经大学统计学院, 甘肃兰州 730020

发布日期:2020-05-06
作者简介:彭波(1993— ),男,硕士研究生,研究方向为金融统计与风险管理. E-mail:m19993082290@163.com*通信作者简介:郭精军(1976— ),男,博士,教授,博士生导师,研究方向为金融统计与风险管理. E-mail:guojj@lzufe.edu.cn
基金资助:
国家自然科学基金资助项目(71561017,71961013);甘肃省飞天学者资助项目

Asset pricing and simulation under the environment of jumping and mixed Gaussian process

PENG Bo, GUO Jing-jun^*

School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China

Published:2020-05-06

摘要/Abstract

摘要： 建立了基于跳环境和混合次分数布朗运动下的欧式期权定价模型。首先,利用Delta对冲原理,获得了欧式期权所满足的随机偏微分方程。其次,使用拟条件期望分别得到欧式看涨、看跌期权定价公式和看涨看跌平价公式。然后,通过希腊字母Δ、 Δ、 ρ、Θ、Γ、ν和关于Hurst指数H的偏导公式量化了资产风险。最后,数值模拟表明:定价参数中的Hurst指数H和跳跃强度λ对期权价值有显著影响。

关键词: 跳扩散, 次分数布朗运动, 拟条件期望, 期权定价, 资产风险

Abstract: The European option pricing model is established by based on mixed sub-fractional Brownian motion in jump environment. Firstly, the partial differential equation satisfying European option can be obtained through the Delta hedging principle. Secondly, the call option, the put option pricing formula and the call-put parity formula are respectively obtained by using the quasi-conditional expectation. Then, the asset risk is further quantified by Greeks Δ, Δ, ρ, Θ, Γ, ν and the partial derivative formula forthe Hurst index H. Finally, numerical simulation show that the Hurst index H and jump intensity λ in pricing parameters have a significant impact on the value of option.

Key words: jump diffusion, sub-fractional Brownian motion, quasi-conditional expectation, option pricing, asset risk

中图分类号:

F224.7

彭波,郭精军. 在跳环境和混合高斯过程下的资产定价及模拟[J]. 《山东大学学报(理学版)》, 2020, 55(5): 105-113.

PENG Bo, GUO Jing-jun. Asset pricing and simulation under the environment of jumping and mixed Gaussian process[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 105-113.

参考文献

[1] BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81(3):637-654.
[2] CHERIDITO P. Mixed fractional Brownian motion[J]. Bernoulli, 2001, 7(6):913-934.
[3] SUN L. Pricing currency options in the mixed fractional Brownian motion[J]. Physica A: Statistical Mechanics & its Applications, 2013, 392(16):3441-3458.
[4] SHOKROLLAHI F, KıLıçMAN A, MAGDZIARZ M. Pricing european options and currency options by time changed mixed fractional Brownian motion with transaction costs[J]. International Journal of Financial Engineering, 2016, 3(1):637-654.
[5] MERTON R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1/2):125-144.
[6] LO A W, MACKINLAY A C. Stock market prices do not follow random walks: evidence from a simple specification test[J]. Review of Financial Studies, 1988, 1(1):41-66.
[7] SHOKROLLAHI F, KıLıçMAN A. Pricing currency option in a mixed fractional Brownian motion with jumps environment[J/OL]. Mathematical Problems in Engineering, 2014[2020-03-19]. https://doi.org/10.1155/2014/858210.
[8] PETERS E E. Fractal structure in the capital markets[J]. Financial Analysts Journal, 1989, 45(4):32-37.
[9] NECULA C. Option pricing in a fractional Brownian motion environment[J]. Mathematical Reports, 2002, 2(3):259-273.
[10] MURWANINGTYAS C E, KARTIKO S H, GUNARDI, et al. Option pricing by using a mixed fractional Brownian motion with jumps[J]. Journal of Physics: Conference Series, 2019(1180):012011.
[11] ROGERS L C G. Arbitrage with fractional Brownian motion[J]. Mathematical Finance, 1997, 7(1):95-105.
[12] 郭精军, 张亚芳. 次分数Vasicek随机利率模型下的欧式期权定价[J]. 应用数学, 2017,30(3):503-511. GUO Jingjun, ZHANG Yafang. European option pricing under the sub-fractional Vasicek stochastic interest rate model[J]. Applied Mathematics, 2017, 30(3):503-511.
[13] 程志勇,郭精军,张亚芳.次分数布朗运动下支付红利的欧式期权定价[J].应用概率统计,2018,34(1):37-48. CHENG Zhiyong, GUO Jingjun, ZHANG Yafang. European option pricing for paying dividends under sub-fractional Brownian motion[J]. Applied Probability and Statistics, 2018, 34(1):37-48.
[14] 肖炜麟,张卫国,徐维军. 次分数布朗运动下带交易费用的备兑权证定价[J]. 中国管理科学,2014,22(5):1-7. XIAO Weilin, ZHANG Weiguo, XU Weijun. Pricing of covered warrants with transaction costs under sub-fractional Brownian motion[J]. Chinese Journal of Management Science, 2014, 22(5):1-7.
[15] TUDOR C. Some properties of the sub-fractional Brownian motion[J]. Stochastics an International Journal of Probability and Stochastic Processes, 2007, 79(5):431-448.
[16] XU Feng, LI Runze. The pricing formulas of compound option based on the sub-fractional Brownian motion model[J]. Journal of Physics: Conference Series, 2018(1053):012027.

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在跳环境和混合高斯过程下的资产定价及模拟

Asset pricing and simulation under the environment of jumping and mixed Gaussian process

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