Constructing a Volatility Risk Premium Using Gaussian Process for Regression

Abstract: In this thesis we investigate the volatility risk premium (VRP) on OMXS30 and S&P 500 and the predictive capabilities of Gaussian Process for regression (GP) on the volatility of those indices. The results are evaluated by comparison with corresponding predictions of a few methods from the GARCH family as well as a naive approach. Several volatility risk premia are constructed using the different forecasting methods, and their explanatory power for stock market returns is analyzed using linear regressions. We found that the one day ahead volatility forecasts made with the GP were not as similar to the realized volatility as those made with the naive approach, and not as good at predicting the direction of change as the comparative GARCH methods. There seems to exist a volatility risk premium on the Swedish market, however not as large as the VRP on the US market, potentially indicating greater risk aversion among investors on the US market. For both markets, the volatility risk premium is found to predict future stock market excess returns, with the VRP constructed from the regular GARCH(1,1) giving the highest adjusted R2.