Testing the Martingale Restriction for Option Implied Densities

This paper contributes to the forecasting literature by presenting a new evaluation method for density and probability estimates. This procedure is particularly well suited for analysing time series of forecasts implied from option prices, although the results are very general and can be applied also outside this framework. A small scale simulation study documents that valid and accurate inference can be drawn for option implied densities with the proposed method. The new testing procedure is demonstrated in an empirical application on density estimates implied from US $/ British pound; currency options