The Variance Process Implied in VIX Options: Affine vs. Non-Affine Models

Abstract

We use the informational content of VIX derivatives to infer implications on the non-affine modeling of the stock returns' variance dynamics. We find that both a non-affine diffusion and variance jumps are necessary to capture the short- and long-term implied volatility distribution. In- and out-of-sample, a linear CEV jump-diffusion model leads to valuation errors that are negligibly affected by the VIX options' maturity and moneyness. For this setup, we obtain parameter estimates that are comparable to the stock option pricing literature. Compared to a linear specification, we find that estimating the diffusion exponent freely does not lead to significantly better results.

Keywords: Jump-diffusion model, volatility derivatives, VIX options, non-affine diffusion

JEL Classification: G13, C58