A View on the Risk-Neutral Density Forecasting of the Dax30 Returns

Option-implied risk-neutral densities incorporate market expectations with respect to the future course of option underlyings. Under the risk neutrality assumption various methods have been developed. In this paper, we look into two of them: parametric mixture of lognormals method and non-parametric Rookley method. We use option data on the DAX30 index. The Berkowitz test is employed to check the goodness of fit of the estimated densities, while we use the llikelihood criterion to compare their performance. Our results show that risk-neutral densities can be good predictors for horizons of 4, 5 and 6 weeks, while for horizons of 2 and 3 weeks the null hypothesis that risk neutral densities are accurate predictors of the distribution of the DAX30 returns is rejected.