Option-Implied Crash Index

Abstract

This paper offers a model-based crash index (CIX) by exploring the pricing difference between out-of-the-money put options and at-the-money options via a jump-diffusion model (SVJ) with stochastic volatility and jump risk.  Analogous to the VIX index as the option-implied volatility, our CIX index is the option-implied mean crash size of the SVJ model.  Empirically, the CIX index is closely related to the non-parametric option-implied skewness, indicating the importance of the crash component.  Moreover, we document a significant upward trend in the CIX index in recent years, which coincides with the increasing trend of investors' crash narratives derived from news coverage.