区域转换随机跳跃与非仿射随机波动率模型下的期权定价  

Option pricing based on regime switching random jump and non-affine stochastic volatility model

作　　者：李奥 范小明[1] LI Ao;FAN Xiaoming(School of Mathematics,Southwest Jiaotong University,Chengdu,Sichuan 610000,China)

机构地区：[1]西南交通大学数学学院,四川成都610000

出　　处：《内江师范学院学报》2025年第4期24-33,共10页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(12371178)。

摘　　要：为了更加准确拟合标的资产价格动态过程,提出一个马尔可夫区域转换随机跳跃模型,并且引入非仿射参数,此外,还考虑随机利率、随机波动率和双指数跳跃幅度对期权价格的影响.在此动态模型下得到欧式看涨期权的解析解,并用数值分析探讨区域转换模型和非仿射模型对期权价格和隐含波动率(IV)的影响.结果表明:当随机跳跃强度的长期均值平均存在区域转换时,会导致期权价格上升与IV增大;当非仿射参数β增大时,期权价格会增大,非仿射参数的增加也会使IV增大,且IV曲线向左产生偏移,初始跳跃强度与初始波动率的增大都会导致IV曲面升高.模型对比分析结果也验证该模型具有稳健性.In order to fit the dynamic process of the underlying asset price more accurately,a Markov region switching stochastic jump model is proposed,and introduces non-affine parameters.In addition,the model also considers the influence of stochastic interest rate,stochastic volatility and double exponential jump amplitude on option price.The analytical solution of the European call option is obtained under this model,and the influence of the region transition model and the non-affine model on the option price and the implied volatility( IV) is discussed by numerical analysis.The fact show that when the long-term average of the random jump intensity has a region transition,it will lead to an increase in the option price and an increase in IV.When the non-affine parameter increases,the option price will increase,and the increase of the non-affine parameter will also increase the IV,and the IV curve will shift to the left.The increase of the initial jump intensity and the initial volatility will lead to the increase of the IV surface.The comparative analysis results of the model also verify that the model is robust.

关 键 词：区域转换 非仿射随机波动率 欧式期权定价 傅里叶变换 

分 类 号：O211.6[理学—概率论与数理统计]