Hi there, I'm a newbie in interest rate derivatives modelling and am currently fighting hard when it comes to the calibration of the Multiple Factor LMM. I am currently searching for an algorithm to calculate the volatilities for each factor. The way I understand it (as I read it in Rebonato's) I think is that the first step would be to calculate the spot volatilities for each caplet which I can derive from the flat cap volatilities from market sources as in Bloomberg for instance. Then, if I choose to build a one factor model I can simply take these calculated "Black" volatilities as inputs for the model. But, if I choose to use the multiple factor lmm I need an algorithm to sort of "strip" the volatilities for each factor. Does anyone know such an algorithm? I've read somewhere that I could use a principal component analysis for this step but I am not sure if that's the best solution for this? Thanks for your help!Cheers,Marco

I remember there is one more methodolgy described in Brigo's book -for full factor model, a parameterized covariance matrix is calibrated to swaptions market. I would search for Brigo's notes on LMM.Hope it helps

Thank you very much for your help. I have just acquired this book and will look for it. But just another short question. Is this a standard approach to use a principal component analysis? Kind RegardsMarco

hi Marco!I guess I am doing the same thing as you are. Yet, is a complete set of caps available in the market so that you can get the volatility of every underlying caplet?The data I have now are like ATM caps with maturities 1y, 2y, 3y, 4y, 5y, 7y and 10y with semi-annual reset...Really have no clue about how to extract the caplet vol now... Linear interpolation would be my last resort...

there are many threads on this exact same problem on wilmott.. the most used methods of extractingcaplet-vols from cap-vols is differencing cap prices to get caplet price and then finding implied volatility

Carol Alexander shows in 'Calibrating the lognormal fwd rate model' that cap volatilities are vega weighed sum of caplet vols. You could use that. Only in same cases you could land up with negative vols...

like in what cases the volatilities can get negative?

As I remember, you'll get problems if you use linear interpolation. The bloomberg cap screen will also provide caplet vols, which are useful if you just need some quick numbers to test your model. Note that they are not so smoothly interpolated, so you'll probably want to eventually generate your own caplet vols using, perhaps, a cubic interpolation. You'll also need to decide how short time frame to interpolate backward from the smallest available market cap vol.

Thank you all for your nice help. After a lot of looking into this I finally found the book: The Libor Market Model in Practice which was co-authored by Dariusz Garatek. It is very good and explains everything very easily. I was no able to calibrate my model co implied caplet volatilities and am currently working on even more advanced techniques.If anyone requires some help on that, please let me know: marco_haefner@web.de