I've backed out a time series of risk-neutral densities of GBP/USD options using a non-parametric approach in Matlab and would like to assess their forecast ability by applying the unconditional test in section 2.3 (page 11) of Christoffersen and Mazzotta "The Accuracy of Density Forecasts from Foreign Exchange Options", JFinEmetr (2005). However, I am not sure how to go about obtaining a series of probability transforms from truncated RNDs. I am also very new to Matlab so any guidance regarding the implementation of Christoffersen and Mazzotta (2005) would be greatly appreciated.
Calculate the cumulative RNDs - these form a bijection from the observed returns through to (0,1). Reverse the map so that a random uniform samples a return from the distribution. Non-parametric sampling that recovers the estimated terminal density goven by vanilla option prices.