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 co-jumps 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.

Keywords: Option pricing, S&P 500 and VIX joint valuation, Higher-order moments, Specification analysis, Model features

JEL Classification: G12,G13