Pricing VIX Futures Under a Markov‐Switching GARCH Framework
提出一个马尔可夫转换GARCH模型来描述VIX指数，并推导出VIX期货的解析定价公式，实证表明加入状态转换能显著提升拟合和定价效果。
ABSTRACT We propose a Markov‐switching GARCH framework to describe the VIX series. Unlike previous studies on derivatives pricing, both the conditional mean and conditional variance here are allowed to vary with the market state described by a hidden Markov chain process. This switching framework preserves the good properties, under which we derive the analytical pricing formula for the VIX futures. In addition, to make it feasible in practice, we design a novel analytical algorithm that can efficiently filter out all the unobserved variables in the model. The empirical studies show that adding the Markov‐switching terms can significantly improve the fit of the underlying VIX series and the pricing performance of the VIX futures both in‐ and out‐of‐sample. Our research highlights the importance of incorporating regime switches that can be viewed as an additional risk factor into the model framework.