As far as I understand, under the Libor Market Model the forward rates are assumed to have a log-normal distribution. Given that I have constructed my LMM model and now have a matrix of:
- k different forward rates, that is, they mature on different dates.
- t time steps
- N different scenarios
How can I make either a chi-squared test or a Kolmogorov-Smirnov test to check for log-normality?
I have already done tests with:
One forward rate, one time-step and all scenarios at a time
One forward r ate, all time-steps and one scenario at a time
These two tests reject the hypothesis that they should have a log-normal distribution, and my question is therefore:
In what way are they assumed to be log-normal, that is, with what part of the data do I test?
Worth noticing is that I simulated under the spot measure, does this matter?