广西师范大学学报（自然科学版） ›› 2021, Vol. 39 ›› Issue (5): 158-172.doi: 10.16088/j.issn.1001-6600.2020121101

• 研究论文 • 上一篇    下一篇

随机利率跳扩散模型下幂型乘积远期生效期权定价

谢冬林, 邓国和*   

  1. 广西师范大学 数学与统计学院, 广西 桂林 541006
  • 收稿日期:2020-12-11 修回日期:2021-03-06 出版日期:2021-09-25 发布日期:2021-10-19
  • 通讯作者: 邓国和(1969—), 男, 湖南桂阳人, 广西师范大学教授, 博导。E-mail: dengguohe@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11461008); 广西自然科学基金(2018GXNSFAA281016)

Pricing Forward-start Power Options with Product of Two Assets in a Stochastic Interest Rate and Jump Diffusion Model

XIE Donglin, DENG Guohe*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2020-12-11 Revised:2021-03-06 Online:2021-09-25 Published:2021-10-19

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摘要： 在随机利率下考虑标的资产价格服从跳扩散过程的两资产幂型乘积远期生效期权的定价。应用Feynman-Kac定理、联合特征函数及Fourier反变换等方法获得了两资产欧式幂型乘积远期生效期权价格的显示解。应用离散快速Fourier变换(FFT)对期权价格进行数值计算, 并应用Monte Carlo模拟法检验了FFT方法的有效性。应用本文方法比较4类市场模型下期权价格的变化情况, 分析幂型乘积远期生效期权价格依赖于标的资产价格的跳跃风险因素、期权生效日与到期日、两资产价格间相关系数、利率的均值回复速度和长期均值水平等主要参数的敏感性。数值结果表明:跳跃风险因素、期权生效日与到期日、相关系数和利率的长期均值水平对期权价格具有较为显著影响, 利率的均值回复速度对期权价格也有一定的作用, 这些结果有利于投资者进行风险管理与对冲。

关键词: 幂期权, 乘积期权, 远期生效期权, CIR随机利率, Girsanov定理, Fourier反变换

Abstract: In this paper, the pricing problem on forward-start power options with product of two assets followed jump diffusion models in a stochastic interest rate framework is considered. Using the Feynman-Kac theorem, the joint characteristic function and the Fourier inverse transformation techniques, the closed-explicit solutions of the European forward-start power options with product of two asset are obtained. Some numerical examples for the option price are implemented by the fast Fourier transform (FFT), and the validity of the proposed method is verified by Monte Carlo simulation. The changes of option price in the proposed model were compared with that of other three different models (Black-Scholes, Merton and CIR+Black-Scholes), and the sensitivity of the price of the forward-start power options with product of two assets to some main parameters were analyzed, including the power factor, jump risk factors, maturity date, the correlation coefficient, average recovery speed and long term average level of interest rate, in the proposed model. Numerical results show that the power factor, jump risk factors, maturity date, the correlation coefficient, and long term average level of interest rate have more significant effect on the option price, and average recovery speed of interest rate has some effects on the option price. These are beneficial to risk management and hedging for investors.

Key words: power option, product option, forward-start option, CIR stochastic interest rate model, Girsanov theorem, Fourier inverse transformation

中图分类号: 

  • O212.1
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[1] 温小梅, 邓国和. 双随机波动率跳扩散模型的复合幂期权定价[J]. 广西师范大学学报（自然科学版）, 2021, 39(2): 101-111.
[2] 邓国和. Heston模型的欧式任选期权定价与对冲策略[J]. 广西师范大学学报（自然科学版）, 2012, 30(3): 36-43.
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