波动率建模及其在金融市场风险对冲中的应用

As a risk mitigation tool ，Volatility Index (VIX) options can provide effective market risk hedging for financial institutions ,they play an important role in preventing the bankruptcy of large financial institutions, they can also stabilize the financial market and promote financial innovation. Theaccurate and quick pricing of index volatility options means a lot to the design and application of indexvolatility productions. Compared to the traditional options and stock options, volatility options havemany unique properties, such as mean reversion, jumps, stochastic volatility, fat tails and skew,which makes modeling much more complex.This project focuses on the VIX options and VXX optionsmodeling, pricing, risk analysis and application,we will put the "LogOU VIX+ Poisson Jump +SR SV"in the form of single-factor model and further extend it to multi-factor model, while the modelsignificantly or semi-explicit solution is given. We will use the market data to calibrate the model andanalyse the stability of the parameters, the calculation speed, the Vol-of-Vol short-term and long-termmemory, as well as the term structure and dynamics of the implied volatility . We will also price the VIXfutures and exotic VIX options in the the VIX model framework and innovate the way of calculating theVolatility Index.We will use the HS300 index, HS300 futures and HS300 options to compute theVolatility Index, which provides a theoretical reference to the development for the Chinese market ofvolatility derivatives.

波动率指数(VIX)期权能为金融机构提供有效的市场风险对冲，对稳定金融市场，促进金融创新有着重要作用。VIX期权的准确快速定价对VIX产品的设计和应用有重要意义。与股票期权等传统的期权比较，VIX期权有很多独特的性质，如均值回复性、跳、随机波动率、厚尾性和偏斜，其建模问题更加复杂。本项目重点研究VIX和VXX期权的建模、定价、风险分析与应用，将构建"LogOU VIX+Poisson Jump +SR SV"形式的单因子模型及多因子模型，同时给出模型的显式解。并利用市场数据对模型进行校正，分析参数的稳定性、计算速度、Vol-of-Vol的长短期记忆性以及隐含波动率的期限结构和动态性质。本项目还将在VIX模型框架下对VIX期货以及奇异VIX期权定价，创新波动率指数构建方式，设计以HS300指数、期货和期权分别或共同构建的波动率指数，从而为发展中国市场的波动率衍生品提供理论参考。

波动率指数（VIX）期权能为金融机构提供有效的市场风险对冲，对稳定金融市场，促进金融创新有着重要作用。基于目前国内外文献中对VIX指数期权定价方面存在很大误差，无法很好的刻画波动率产品的正向隐含波动率偏斜等情况，项目组从一致性和独立性两类模型出发，创新式的提出MRLRSVJ、3/2跳扩散随机波动率模型、马氏调制的状态转换随机波动率模型、4/2随机波动率模型等，丰富了现有市场上定价模型，大幅提高VIX等波动率期权的定价准确度。另外，项目组首次提出VXX期权的定价方法，将信用违约风险因子和期权定价很好的结合，提出带违约风险的3/2跳扩散随机波动率模型。同时项目组在VIX定价框架下构建了包括外汇期权、实物期权等相关金融衍生品的随机波动率模型，均有不错的定价效果。在levy过程的框架下，更进一步推广了考虑随机波动率和杠杆效应的资产定价模型。同时，项目组对期权的数值解法进行了更深入的研究，采用常用的Monte Carlo方法进行优化，提出block adjoint method、Forward-path method等更加简洁快速的方法，提高期权定价速度。最后，在对波动率产品建模的基础上，项目组考虑波动率曲面建模和中国市场波动率特征，对中国与美国股票市场的波动溢出效应进行度量，刻画中国的新兴市场与成熟市场间波动性的相互影响。