Alternative Model Specifications for Implied Volatility Measured by the German VDAX

Alternative Model Specifications for Implied Volatility Measured by the German VDAX In this paper, two nested model specifications for the stochastic behavior of the German stock market volatility index VDAX are compared based on a sample of index observations. Following the literature, the well-known mean reverting diffusion model serves as the standard model specification. The second model specification is an extension which allows for discontinuous changes in the series. The estimation results for the VDAX indicate that the empirical observations do not confirm the moment restrictions given by the standard model. While, at the given confidence level, this yields to a rejection of the mean reverting diffusion model, the extended specification cannot be rejected providing significant evidence of a positive jump component. An application of the mean reverting jump diffusion model is given in a risk-neutral option pricing framework. Simulated option prices reveal economically and statistically significant price differences not only depending on the choice of the model specification but also due to the consideration of the jump component itself. (JEL C13, C15, C22, G13