Nothing to do with pdes or numerics but simple relationship between credit ratings over one period and ratings over another period results in exponential of a transition prob matrix.

So we can now blame the credit crisis on software engineers!

P

Back to topic.

Yes, did they use the Python/APL approach? I wonder in which language they do MBS. A little knowledge is a dangerous thing.

Your remark is a very good example; From the

* infinitesmial generator matrix *[$]Q[$] we can compute the 1-step

*transition probability* matrix [$]P[$]:

[$]P(t, t + dt) = I + dtQ + o(dt)[$]

Now compute to [$]s = t + mdt[$] (m-period) to get a matrix polynomial (or is it polynomial matrix

) and then let [$]m[$] go very big to get

[$]P(t, s) = e^{(s-t)Q}[$]

This can now be computed by one of the 19 methods of Moler and Van Loan.

I have not given any definitions of the italicized words; for maximum flexibility you can fill in your own.

https://en.wikipedia.org/wiki/State-transition_matrix