Implied Volatility and Extracted Risk Neutral Density of VIX Options during the Crisis and Relatively Calm Periods

The 2008 financial crisis provides a valuable opportunity to study empirical data of market volatility during severe financial crisis. In this thesis, we study the implied volatility of VIX options during the crisis (2008) and a relatively calm period (2011). We present a method of calculating the implied volatility of VIX options and fit the implied volatilities using a 4th degree spline interpolation and propose method of extracting risk neutral density from fitted data. We analyze the slope and the level of the fitted implied volatility of VIX options during those periods. The results show that the level of the implied volatility of VIX options is higher and the slope is flatter during the distressed market compared to the relative calm periods