Extracting, Evaluating and Combining Density Forecasts for Stock Index Returns Using Option Contracts and Historical Index Prices

This research shows how to extract, evaluate and combine density forecasts of stock index returns from option contract prices and historical index prices. Option implied density forecasts are extracted using both theories of risk-neutral valuation and the specification of a semi-parametric option pricing model. A novel approach is introduced to transform the option implied risk-neutral density forecasts obtained, into real-world density forecasts. The latter are therefore calibrated through the transformation and accounts for the subjective attitude toward risk of investors. Historical densities are derived based on the specification of a model of conditional volatility and the distribution of the error terms of the data generating process. The Kullblack Liebler information criterion (KLIC) is used in this research as a measure of the distance between the true unknown density forecast and the empirical densities derived for horizon one day ahead to sixty days ahead. Studying the extraction and the evaluation of density forecasts for stock indices based on the two sources of information mentioned above can be useful to academic, practitioners and policy makers such as central banks to understand the relevance of the type of information used for the forecasting exercise and the pertinence of the theoretical or empirical assumptions justifying the forecasting methodology. This thesis suggests that historical density forecasts outperform both option implied risk-neutral and real-world calibrated density forecasts in the KLIC sense. This means based on the results obtained in the KLIC based methodology and the subsequent predictive ability tests, historical density forecasts are more appropriate for multiple horizon density forecasts of return than both simple and advanced option implied density forecasts.