The Empirical Performance of Option Based Densities of Foreign Exchange

In this study we first estimate the volatility diffusion process of the underlying futures contracts that fit best daily observed American option prices. We then calculate for each day risk neutral densities for different points of time in the future by simulating these processes. To assess how good these denisities are in forcasting, we suggest non-parametric tests based on the inverse probability function. These tests account for the correlation of the inverse probabilities due to the overlapping window problem that always arises when the forecasting horizon is longer than the sample frequency. We find that our densities do considerably well for the thirty to sixty day horizon while doing less well for shorter horizons.