What is the real reason to use C here?
The real reason is that it was just an idea that we came up with and decided to try it. It worked well, so we stuck with it. :)
Another fast monte carlo anecdote: at Bloomberg they are doing this sort of thing with GPUs.
http://www.wallstreetandtech.com/it-infrastructure/bloomberg...
I'm wondering if maybe you're doing way too many simulations in the calibration, do you really need more than a few hundred to a thousand or so? The 0.1 quantile is reasonably well separated from 0, and I would have expected you'd get "good enough" convergence pretty quickly.
Also: "we can compare our computed p-value of 11% to our simulated 10% result to determine whether or not the model is accurate enough." you're getting a full pdf out of the simulations, are you also comparing to the full distribution of your test statistics?
Monte-Carlo is more meaningful than using some sort of chi-squared. But why is it faster?
