传统跳-扩散期权定价模型假设跳跃行为和波动率之间或独立演化、或仅单向反馈。近年来研究表明，股市中随机跳跃和连续性波动不仅自身具有持续性，还会对彼此演变产生非对称的交叉回馈作用，这一特征亦影响到衍生品的定价。本项目将结合特征函数傅里叶数值方法、序贯蒙特卡罗模拟技术以及局部风险中性测度变换等手段，同时考虑股票价格跳跃自激发与波动率集聚效应，拟构建具有调和稳态跳-扩散双因子交叉回馈机制的期权定价模型，在分析方差平稳性和风险中性等价关系的基础上，应用于国际期权市场，并进行参数估计、模型校准和误差分析，继而与传统跳-扩散随机过程、时变Levy过程、双成分模型、Hawkes跳跃集聚模型和Levy-GARCH模型进行比较研究。本项目将联合股票市场与期权市场信息，系统地阐述股市中跳-扩散风险的演变规律，为现代资产定价、投资分析和风险管理提供理论参考和实践指导。

Traditional jump-diffusion option pricing model assumes jumps and volatility are isolated or one-way feedback only. In recent years, studies have shown that stochastic jumps and volatility both have long memory, and would have asymmetric cross-feedback effects on each other’s evolution, which is also well demonstrated in options market. Combined with numerical FFT, sequential Monte Carlo simulation as well as the local risk neutral valuation, this project proposes a new jump-diffusion model driven by tempered stable infinite activity processes, in which jump self-exciting and volatility clustering together with cross-feedback mechanism are totally considered. Based on the analysis of variance stationary and equivalent risk neutral relationship, it is used in China and the United States market for parameter estimation and model calibration. This project also illustrates a comparison of option pricing performance between the jump-diffusion stochastic process, double-factor and component model, time-changed Levy process, Hawkes jumps model and Levy GARCH model. This project intends to jointly use the information in the stocks and options markets to evaluate the jump-diffusion risks and draw their evolution law in financial system, which would provide a significant theoretical reference and practical guidance for modern asset pricing, risk management and investment analysis.