Application of model combination to forecast the implied volatility surface

The aim of this thesis is to explore predictable dynamics in the implied volatility surface of S&P500 index options. I consider three approaches to modelling the surface that can be distinguished in the literature: (i) dynamic factor model where the latent factors drive the dynamics of the surface, (ii) models that assume parametric structure of the surface, (iii) option pricing model consistent with the skew observed for the implied volatilities. I fi that the latent factor model provides the best accuracy in most regions of the surface at investigated one-day ahead forecasting horizon. This model combines two-step estimation procedure by means of Principal Component Analysis and VAR model for factor dynamics, with non-parametric Nadaraya-Watson regression that allows to deal with special design of implied volatility data. Forecasting accuracy can be further improved by using combination forecast methods. I implement combining methods based on equal weights, discounted mean square prediction error, and optimal estimated weights. Combining based on the estimated optimal weights yields improvement over the individual models in all regions of the surface. However, neither the individual models nor the combination models are capable of beating random walk forecast, a simple forecast that assumes that tomorrow’s value of implied volatility equals its current value.