I'm trying to calibrate a Libor Market Model (LMM) in Matlab with my user-defined function, not their package.

I already fitted the market volatilities using SABR but failed to simulate the correct market prices.

Here are my questions:

  • Has anyone a validation set of cap surfaces and cap prices?

  • What are the quoting market conventions for pricing using a Libor curve? I've seen many different ways of applying discount on the black formula. What about OIS?

  • Is there any really good implementation guide available, with pseudo or real code to observe?


For LMM I thing the Rebonato's book 2002 is a good reference. He has explained the condition of vol quotation that allow existence of calibration solution.

LMM parameters and inputs are quite complexe, calibrator not work maybe caused by your implementation's bugs but not only data input. I think it is better if you calibrate virtually before true market data. I.e you create the data yourself so that you know the "true parameters", you calibrate from a "false parameters" to find the true one. If this first step work, you can say your implementation do not have bug.

The second step is then read article, improve the model by ensuring always the virtual test works.

If that always not work with market data, maybe it is caused by bad data. You can prove it by using the cascade calibrattion (Brigo Damien 2006 book). If effectively data is bad, you need to add a regulation into the calibration (penalty method). However be aware that adding penalty modify the solution (wich is allowable when exacte solution do not exist), you have to study how and "how much" penalty you add in order to have the reasonable accuracy.

PS : I had a litle experience in implementing LMM , we use swapfion vcub and standard discount curve as input for calibration.

  • $\begingroup$ That's a good solution to the problem. I'll try and see how that goes. Another thing is, I already read both of renobattos book and it all make sense but I mean coding wide its troubling me. Do have any code guide on it? $\endgroup$ – Tulio Carnelossi Jan 12 '15 at 10:32

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