随机波动率模型下的VIX期权定价

The Vix Option Pricing Based on Stochastic Volatility Models

本文主要有两部分:第1部分找到一个拟合VIX指数能力较优的随机波动率模型;第2部分是在较优模型下讨论VIX指数期权定价问题.其中第1部分首先利用非参数方法估计随机波动率模型的漂移项和扩散项,然后在此基础上对七个经典随机波动率模型进行拟合和比较.第2部分在较优模型基础上加上跳跃,讨论期权定价的PDE和解析解.

This article mainly has two parts： the first part finds a model which has a better ability to capture the behavior of the vix than others. The second part discusses the vix option pricing under the better model In the first part, using a nonparametric method, this paper estimates the draft and diffusion items of stochastic volatility models. Then this paper estimates and compares seven continuous time volatility models. In the second part, the optimum model we get in the first part will be turned into a jump-diffusion model and then the partial differential equation and analytical solution of the option pricing are discussed under the optimum jump-diffusion model.