i am at starting stage of LMM implementation (non-param calibration, piecewise constant)when using LMM to price vanilla caps, i know it can recover black model price.but during this process, i do not need to use the instantaneous correlation matrix. (i can get black price)it seems to me that forward rates in caplet pricing are assumed to be independent?But the purpose of calibration is find out the corr matrix so that i can generate random numbers with desired correlationwhat's wrong with my understanding here?alsoi calibrate LMM to cap, swaption quotes as follows1. obtain caplet vol from market quoted cap vol (by stripping)2. from swaptions quotes, minimize the diff between market swaption quotes and my swaption prices by searching fora fitting instantaneous correlation matrix

QuoteOriginally posted by: james88when using LMM to price vanilla caps, i know it can recover black model price.but during this process, i do not need to use the instantaneous correlation matrix. (i can get black price)it seems to me that forward rates in caplet pricing are assumed to be independent?But the purpose of calibration is find out the corr matrix so that i can generate random numbers with desired correlationwhat's wrong with my understanding here?Correlation is needed when you need to price swaptions because the fwd swap rate depends on several fwd rates observed at the same time. In the case of caps, the caplets are independent options (different underlying and also different observation time). That's why you model fwd rates independently.