基于VIX的波动率风险溢价估计

Estimation of the Volatility Risk Premium Based on VIX

波动率风险溢价的估计是资产定价的核心问题之一.本文建立VIX指数与GARCH扩散模型中隐波动率之间关系,继而采用S&P500与VIX指数联合数据,给出GARCH扩散模型客观与风险中性参数的基于有效重要性抽样(EIS)的联合极大似然(ML)估计.进一步,利用粒子滤波方法给出隐波动率的估计,推断VIX隐含的波动率风险溢价.蒙特卡罗模拟实验表明,提出的估计方法是有效的。采用实际数据进行的实证研究表明,波动率风险溢价小于零,这意味着市场对波动率风险具有负的定价。

One central problem in asset pricing is the estimation of the volatility risk premium.By liking the VIX index to the latent volatility for the GARCH diffusion model,an efficient importance sampling(EIS) is developed based on joint maximum likelihood(ML) estimation method for the objective and risk-neutral parameters of the GARCH diffusion model using joint data on the S&P500 and VIX index.Then,a particle filter-based estimation method is developed for the latent volatility,and hence the volatility risk premiums implied by the VIX is infered.Monte Carlo simulation study shows that the proposed method performs well.Empirical results demonstrate that the volatility risk premium is negative,which implies the volatility risk is negatively priced by the market.