We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK


93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > A multi-horizon comparison of density forecasts...
View graph of relations

« Back

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

Research output: Contribution to journalJournal article


Journal publication date11/2010
JournalJournal of Banking and Finance
Number of pages16
Original languageEnglish


We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.