An examination of the continuous-time dynamics of international volatility indices amid the recent market turmoil

Volatility indices have been designed for many markets as gauges to measure investors' fear of market crash. The recent market turmoil has produced historically high volatility levels. We take a look at the behavior of the VIX and VSTOXX indices by including the recent market turmoil into the data. We estimate various continuous-time models with focus on the structure of the drift and diffusion functions. Two methodologies are utilized: the maximum likelihood estimation, and Aït-Sahalia's parametric specification test. While the results from the parametric specification test advocate strongly for specifying more flexible drift and diffusion functions, nonlinear drift structure often only adds negligible benefit in terms of the likelihood function value. Simulation is carried out to study the finite sample bias and jump omission bias. Our results call for caution against finite sample bias when adopting a particular model or fixing a particular parameter vector.