跳跃自激发与非对称交叉回馈机制下的期权定价研究

跳跃集聚和波动率非对称回馈是股票价格运动过程中不可忽视的重要特征.基于动态跳-扩散半鞅随机过程,本文提出了具有时变跳跃到达率和波动率的双因子交叉回馈机制的期权定价模型,推导了跳-扩散交叉回馈模型的一般化风险中性变换关系;同时借助序贯贝叶斯方法对模型和跳跃风险溢价进行校准,并对道琼斯工业平均指数(DJX)、标普500指数(SPX)、苹果(APL)、IBM、JP摩根(JPM)股票进行实证研究,研究发现,它们的跳跃达到率和波动率都呈现集聚性和非对称回馈效应,且跳跃到达率具有更强的持续性和更大的杠杆系数;跳跃风险溢价在定价中占主要地位.期权定价的实证研究还表明,双因子交叉回馈模型具有最小的期权定价误差,定价能力明显优于单向回馈的跳-扩散模型.

Option pricing for the dynamics of jump-diffusion model with jump self-exciting and asymmetric cross-feedback

Jump clustering and volatility asymmetric feedback are important features in stock markets. This paper studies the option pricing issues for a dynamics of jump-diffusion process, which considers the mechanism of time-varying jump arrival rates, diffusion volatility clustering and the asymmetric cross-feedback effect. First, this paper presents the no-arbitrage conditions of equivalent martingale measures for the general jump-diffusion process based on local risk neutral valuation relationship; and then estimates the parameters and jump risk premium of the dynamic jump-diffusion model using the sequential Bayesian learning approach; Finally is the empirical research on the standardized European options of S&P500 Index and Dow Jones Industrial Average, APPLE, IBM and JP Morgan. Our study shows the significant evidence of the jump self-exciting, volatility clustering and asymmetric cross-feedback; these jumps also have a higher persistent influence and show a greater leverage effect to the stock markets; the dynamics of the cross-feedback jump-diffusion model have better performance in option pricing compared with these one-way-feedback jump-diffusion models. Jump risk premium is significantly higher than that of diffusion risk, which plays a dominant role in the process of asset pricing.