An Empirical Comparison of Continuous-Time Models of Implied Volatility Indices

Abstract

We explore the ability of alternative popular continuous-time diffusion and jump diffusion processes to capture the dynamics of implied volatility indices over time. The performance of the various models is assessed under both econometric and financial metrics. To this end, data are employed from major European and American implied volatility indices and the rapidly growing CBOE volatility futures market. We find that the addition of jumps is necessary to capture the evolution of implied volatility indices under both metrics. Mean reversion is of second order importance though. The results are consistent across the various metrics, markets, and construction methodologies.

Keywords: Continuous time estimation, Conditional characteristic function, Implied volatility indices, Volatility derivatives, VIX futures

JEL Classification: C13, C50, G10, G13