A New Model for the Joint Valuation of S&P 500 and VIX Options: Specification Analysis

Abstract

Analyzing the specifications of pricing models for the joint valuation of S&P 500 and VIX options, I find that the existing models cannot adequately represent the two options markets. I introduce a new factor that controls the higher-order moments of the risk-neutral return distribution. The model I propose significantly outperforms all other alternatives, and particularly improves on the benchmark two-variance-factor model with cojumps by 23.66% in-sample and 31.64% out-of-sample. The performance analysis shows that the better fit results from improvements in the modeling of both S&P 500 and VIX options, highlighting the model features that are critical for reconciling the two markets. This paper was accepted by Kay Giesecke, finance. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72233003 and 72303233]. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.00327 .