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I have tested a bit the new LMM process and I have some questions on it.
1- Why th first forward is set to start at time zero and not at any time?
If you have a general schedule not starting today? Do I need to interpolate rates?
2- The simulated forwards are very good (and also caplets) for maturities shorter than 5y-8y. But if the mk caplet volatility is not well behaved (or sufficiently smooth) the process crasches during the costruction of lambdas:
In fact if vol2 = vol(i)*vol(i)*t(i) is smaller then vol1 = vol(i-1)*vol(i-1)*t(i-1) then l = vol2- vol1 <0 and sqrt(l/delta(i-1)) crashes. Dou you have any ideas? Do you think could be possible to use a parametric version of caplet volatility?
3- Why does the drift function take the deltas instead the accrual periods? I think it should use the accrual period instead, due to the fact that: P(ti, ti+1) = 1/(1+ delta(i)*Fi) and the delta should be the accrual period on which the forward is built.
thanks in advance,
enrico
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