随机利率随机波动率混合指数跳扩散模型下的期权定价

doi:10.12341/jssms21596

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (8): 2207-2234.DOI: 10.12341/jssms21596

• • 上一篇

随机利率随机波动率混合指数跳扩散模型下的期权定价

吴胤昊¹, 陈荣达^1,2, 汪圣楠¹, 俞静婧¹

1. 浙江财经大学金融学院, 杭州 310018;
2. 嘉兴学院, 嘉兴 314001

收稿日期:2021-10-25 修回日期:2022-02-27 发布日期:2022-10-18
基金资助:
国家自然科学基金重点项目(71631005)资助课题.

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吴胤昊, 陈荣达, 汪圣楠, 俞静婧. 随机利率随机波动率混合指数跳扩散模型下的期权定价[J]. 系统科学与数学, 2022, 42(8): 2207-2234.

WU Yinhao, CHEN Rongda, WANG Shengnan, YU Jingjing. Option Pricing Under the Mixed-Exponential Jump Diffusion Model with Stochastic Interest Rate and Stochastic Volatility[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(8): 2207-2234.

Option Pricing Under the Mixed-Exponential Jump Diffusion Model with Stochastic Interest Rate and Stochastic Volatility

WU Yinhao¹, CHEN Rongda^1,2, WANG Shengnan¹, YU Jingjing¹

1. School of Finance, Zhejiang University of Finance and Economics, Hangzhou 310018;
2. Jiaxing University, Jiaxing 314001

Received:2021-10-25 Revised:2022-02-27 Published:2022-10-18

文章在Heston模型的基础上同时将随机利率与混合指数跳引入模型,并且考虑到金融市场中已存在的负利率事实,因此不同于经典的CIR假设,文章放松了利率不能为负的限制,假定其满足Hull-White过程,提出了Heston-HW-MEJ混合模型.在模型的求解方面,文章推导了含对数价格特征函数的定价半闭解,并采用快速Fourier变换方法进行计算.数值分析的结果表明,文章提出的模型较好地捕捉了尖峰厚尾、盈亏不对称等市场特征与隐含波动率曲面形态,并且快速Fourier变换方法求解相比于Monte Carlo模拟快速、高效.最后通过香港恒生指数期权市场与上证50ETF期权市场数据对多个模型进行了实证比较,结果表明,文章的模型在低利率市场具有更好的定价效果,但在利率相对较高的市场略差于Heston-CIR-MEJ模型.

关键词： 期权定价, Heston-HW-MEJ 混合模型, 特征函数, 快速Fourier变换

Based on Heston's model, this paper introduces stochastic interest rate and mixed exponential jumps into the model. And taking into account the fact that there is already negative interest rate in the financial market, this paper tries to relax the restriction that interest rate cannot be negative, assuming that it satisfies the Hull-White process which is different from the classical CIR hypothesis. Finally, the hybrid Heston-HW-MEJ model is proposed. However, the complexity of the multi-stochastic element system makes the closed-form solution usually does not exist, so in terms of model solving, this paper adopts the fast Fourier transform method to obtain the semi-closed solution of pricing containing the characteristic function of logarithmic price, which is the main work of this paper to derive this characteristic function. The results of numerical analysis show that the model proposed in this paper captures the market characteristics well, such as heavy tail, leverage effect, profit and loss asymmetry, etc, and the fast Fourier transform method is fast and efficient compared with Monte Carlo simulation in solving. And in comparison with the Black Scholes model, the call option prices obtained from the Heston-HW-MEJ model are higher, indicating that the Black Scholes model underestimates the volatility of the underlying, and the Heston-HW-MEJ model implies greater market uncertainty. Finally, through the data of Hong Kong Hang Seng Index option market and Shanghai 50ETF option market, the empirical comparison of several models shows that the model in this paper has better pricing effect in low interest rate market, but it is slightly worse than the Heston-CIR-MEJ model in relatively high interest rate market.

Key words: Option pricing, hybrid Heston-HW-MEJ model, characteristic function, fast Fourier transform

MR(2010)主题分类:

91B28
65C30

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