# Probability integral transforms of risk-neutral densities

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.

• This is wierd,, the public (SSRN) version of Christoffen and Mazzotta does not have a section 5b. What kinds of "probability transforms" does it use? – noob2 Oct 20 '17 at 17:37
• Sorry, it should be section 2.3 (page 11) in the SSRN version. I have edited my question to make the correction and have also provided a link to the paper. – user51462 Oct 20 '17 at 22:26

• Thanks for your answer James, I think it cleared up a lot. I am not sure I understand how the 'uniform' probability transform is related to the cdf, I saw this expression in a paper: $U_{t, h} \equiv \int_{-\infty}^{S_{t+h}}f_{t, h}(u)du\equiv F_{t, h}(S_{t+h})$. The right-hand side makes sense but I don't quite know how that is equivalent to the uniform probability transform, $U_{t, h}$. – user51462 Oct 21 '17 at 0:06