基于4/2-CIR模型的欧式期权定价及实证研究  

Pricing and Empirical Research on European Option under 4/2-CIR Model

作　　者：郭精军 马爱琴 张翠芸 GUO Jingjun;MA Aiqin;ZHANG Cuiyun(School of Statistics and Data Science,Lanzhou University of Finance and Economics,Lanzhou 730020,China;Centre for Quantitative Analysis of Gansu Economic Development,Lanzhou 730020,China)

机构地区：[1]兰州财经大学统计与数据科学学院,甘肃兰州730020 [2]兰州财经大学甘肃经济发展数量分析研究中心,甘肃兰州730020

出　　处：《运筹与管理》2024年第3期162-168,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(72361016,72061020);甘肃省教育厅“双一流”科研重点项目(GSSYLXM-06)。

摘　　要：在假设波动率服从均值回复过程的条件下,探讨了具有随机利率的4/2随机波动率模型下的期权定价问题。首先,基于4/2随机波动率模型提出4/2-CIR随机混合模型,并利用快速傅里叶变换方法推出4/2-CIR随机混合模型下的欧式期权定价公式。其次,通过数值分析的方法,对比4/2随机波动率模型与4/2-CIR随机混合模型的定价结果,分析新模型的定价性能,并运用交叉验证法,对模型中参数进行敏感性分析。最后,选取上证50ETF期权数据进行实证分析。研究发现:随机利率对模型定价结果具有显著影响;期权价格对利率的波动率参数不敏感,而对其它参数都较敏感;与经典B-S模型及4/2随机波动率模型相比,4/2-CIR随机混合模型的定价误差更小,定价结果更接近真实值。With the increasing number of endogenous and exogenous shocks,the financial market has entered an unprecedented period of instability,which increases the financial market risk.As an important financial derivative product,option can effectively hedge the market risk,and the key to using option to hedge the market risk is to price it reasonably.The core of the research on option pricing is to construct a model that fits in with the dynamic change characteristics of the underlying asset.The uncertainty of the future of the financial market keeps the price of financial assets appreciated or depreciated,that is,the volatility of the underlying asset price of the option is not a definite constant but has a certain degree of volatility.Therefore,in order to ensure the reliability of the option pricing results,in the process of constructing the pricing model we must take into account the stochastic volatility characteristics of the underlying asset price.In addition,with the continuous change in national economic policies and financial market conditions,the market interest rate is no longer a constant.An accurate description of the stochastic characteristics of market interest rates is conducive to improving the pricing accuracy of financial derivatives.Therefore,how to accurately describe the dynamic process of financial asset prices and the stochastic fluctuation characteristics of interest rates is an urgent problem to be solved.In this paper,we fully consider the dynamic change characteristics of financial asset prices and the impact of interest rate stochasticity on the pricing results of the option pricing model,and explore the option pricing problem under the 4/2 stochastic volatility model with stochastic interest rate under the assumption that the volatility obeys the mean-reverting process.Firstly,based on the dynamic characteristics of financial asset prices and the randomness of interest rates,the 4/2-CIR stochastic hybrid model is constructed,and the characteristic function of the underlying log asset price

关 键 词：4/2-CIR随机混合模型 期权定价 快速傅里叶变换 敏感性分析 

分 类 号：O212[理学—概率论与数理统计]