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question about libor-market-model

Posted: February 3rd, 2014, 2:21 pm
by kelang
Hi All,I am puzzled with one simulation question under libor-market-model. Could anyone share some intuition on this? I might be very stupid to miss something...Suppose the model has been calibrated successfully under spot-rolling numeraire, now I would like to double check simple European swaption prices using Monte Carlo simulation. Assuming the European swaption matures at T, with the underlying swap tenor of S.Now, given the calibrated libor model and the initial libor, I simulated N libor path, each path contains M steps which simply coincides with cashflow dates.Then I am doing the following two different processes to compute the European swaption prices,a) At the simulation time T which coincides with swaption maturity, obtaining the option value by averaging over the in-the-money swap prices computed using the simulated libor paths at simulation time T, then discounting the option value back to m2mb) Rolling back from the simulation time T+S, which coincides with underlying swap maturity, for each coupon period, calculating the cashflow using the libor path simulated at coupon period starting date, and discounting back to coupon period starting date. Repeating the process until the swaption maturity, then averaging over the in-the-money swap prices to get the option value and discounting back to m2mWhile a) is pretty straightforward and gives the correct prices, b) gives incorrect prices. I cannot tell immediately what's wrong with b)... Anybody knows why?Thank you very much.

question about libor-market-model

Posted: February 3rd, 2014, 4:59 pm
by piterbarg
in b) your exercise decision at T is based on the realized values of future cashflows, i.e. the information that is not available at time T but will be revealed later. That's why the value is different (and wrong). You have to base your exercise decisions at T only on what you will know at T -- which the the swap value at T, i.e. the average of all posible realizations of cash flows from T onwards (not on one particular path)Vladimir

question about libor-market-model

Posted: February 3rd, 2014, 5:09 pm
by kelang
QuoteOriginally posted by: piterbargin b) your exercise decision at T is based on the realized values of future cashflows, i.e. the information that is not available at time T but will be revealed later. That's why the value is different (and wrong). You have to base your exercise decisions at T only on what you will know at T -- which the the swap value at T, i.e. the average of all posible realizations of cash flows from T onwards (not on one particular path)VladimirThank you very much, Dr. Piterbarg.Yes, it makes total sense. This also explains why in my test, vanilla bond/swap prices converge under the above two approaches, but only option prices don't.Thank you again.J