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

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>11/2010
<mark>Journal</mark>Journal of Banking and Finance
Issue number11
Number of pages16
Pages (from-to)2678-2693
Publication StatusPublished
<mark>Original language</mark>English


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.