Forecasting the density of oil futures

Forecasting the density of returns is useful for many purposes in finance, such as risk manage- ment activities, portfolio choice or derivative security pricing. Existing methods to forecast the den- sity of returns either use prices of the asset of interest or option prices on this same asset. The latter method needs to convert the risk-neutral estimate of the density into a physical measure, which is computationally cumbersome. In this paper, we take the view of a practitioner who observes the implied volatility under the form of an index, namely the recent OVX, to forecast the density of oil futures returns for horizons going from 1 to 60 days. Using the recent methodology in Maheu and McCurdy (2011) to compute density predictions, we compare the performance of time series models using implied volatility and either daily or intra-daily futures prices. Our results indicate that models based on implied volatility deliver significantly better density forecasts at all horizons, which is in line with numerous studies delivering the same evidence for volatility point forecast.