VIX Based Stochastic Volatility Models in State Space Form

Stochastic volatility models recognize volatility as a random process with high autocorrelation. In this thesis I incorporate the VIX index in stochastic volatility models in state space form. I develop several models, in which the VIX either is an observed or a state variable. I compare these new models with a standard state space volatility model that extracts the volatility from returns of the S&P500 index. When estimating the latent volatility via the observed VIX series the VIX almost perfectly represents the latent volatility. A volatility estimate based on the VIX index takes higher values than the volatility estimate based on S&P500 returns. On the other hand, volatility based on the VIX as a state variable takes lower values than the S&P500 returns volatility estimate. Evaluating the volatility models with a Value at Risk measure I find that the latent volatility based on the VIX index, which contains a volatility risk premium, is the only volatility estimate to forecast a 1% and 5% Value at Risk correctly on a daily basis during the global financial crisis period.