基于多元Hawkes跳跃互激发与波动率交叉回馈过程的期权定价研究

为捕获多资产、跨市场间的波动溢出、跳跃传导与非对称交叉回馈现象，本项目拟构建多元Hawkes跳跃互激发与波动率交叉回馈的动态跳扩散过程进行期权定价研究。项目首先深入分析研究不同资产、不同市场之间的风险传染以及价格传导机制，全面刻画多个基础资产的联合演变特征；其次，基于随机折价因子结构和跨市场一般均衡条件，研究论证联合风险中性关系，提出多资产无套利定价框架；然后，借助序贯贝叶斯推断和神经网络中的深度学习方法，实现模型的动态选择、联合估计、预测训练和自主学习，以精准捕捉跳跃风险传导路径和渠道；最后，将之与传统的跳-扩散过程、多维CGARCH模型、时变Levy过程、Levy-GARCH模型、多元Copula方法、CoVaR以及空间计量模型等前沿工具进行实证比较分析，在全球范围内综合考察模型和方法在期权定价方面的适用性及优越性。本项目可拓展多资产期权定价框架，为国际化资产配置提供新视角和新方法。

In order to capture the phenomena of volatility spillover, jump propagation and the asymmetric cross feedback in assets and markets, this project intends to construct dynamic multivariate Hawkes process with jump exciting and volatility feedback to study the option pricing. Firstly, the project plans to deeply analyze the mechanism of risk contagion and transmission within different assets and markets, and then describe the characteristics of assets movement. Secondly, the project is going to demonstrate the multi-asset risk-neutral relationship and show a joint no-arbitrage pricing framework based on the cross-market general equilibrium with their stochastic discount factors. Then, with the help of sequential Bayesian inference and deep learning methods in neural networks, dynamic model selection can be realized, and dynamic parameters and potential variables are able to be jointly estimated, accurately quantifying the transmission or direction of jump risk. Finally, the project intends to carry on rich empirical comparative analysis and compare with jump-diffusion process, multi-CGARCH model, time-varying Levy process, Levy-GARCH model, multiple Copulas, CoVaR and spatial econometric model, on a global scale in option pricing about the applicability and superiority. Our project will expand the asset pricing model framework, and provide new ideas and methods.