Density forecast evaluation and the effect of risk-neutral central moments on the currency risk premium: tests based on EUR/HUF option-implied densities

In this paper we estimate risk-neutral probability density functions from EUR/HUF currency options using the Malz (1997) method. First, we compare different option-based indicators. We present so-called 'shortcut' indicators, i.e. indicators that can be calculated directly, without the estimation of RNDs, but which show strong co-movement with the central moments of estimated densities. We also find that it is possible to construct probability-based indicators, which again exhibit strong correlation with the central moments. We present evidence that risk-neutral densities do not provide accurate forecasts for the distribution of the historical EUR/HUF exchange rate. The higher moments of risk-neutral densities are responsible for the rejection of forecasting ability. Our interpretation is that the standard deviation, the skewness and the kurtosis of the risk-neutral densities are significantly higher than the central moments of subjective densities. Finally, we show that the higher moments of risk-neutral densities are able to explain a significant part of the variability in the estimated risk premium. These latter results suggest that risk-neutral standard deviation and skewness can be used as proxy variables for the respective central moments of subjective densities.