Testing and Diagnosing Libor Market Model Calibration
Summary
The document discusses validating a user-built Libor Market Model implementation when calibration to market volatility inputs does not reproduce cap prices. It recommends separating implementation errors from market-data or calibration problems by first generating synthetic prices from known model parameters, then attempting to recover those parameters from altered starting values. If this controlled test fails, the implementation or calibration procedure needs further investigation before market results can be interpreted.
If synthetic tests work but market calibration does not, the inputs may be inconsistent or an exact fit may not exist. The answer points to staged calibration and penalty regularization as possible tools, while cautioning that penalties change the fitted solution and their size must be assessed for accuracy. The discussion also references a standard LMM text for volatility quotation and mentions swaption volatility and discount curves as calibration inputs. It does not provide a validation dataset, implementation code, or a definitive market convention.
Key ideas
- Use synthetic data with known parameters to test whether an LMM calibrator can recover them.
- A failed synthetic test suggests an implementation or calibration issue rather than bad market data.
- Failure on market data after synthetic validation can indicate inconsistent inputs or the absence of an exact fit.
- Staged calibration and penalty methods may help, but penalties alter the solution and require scrutiny.
- The answer gives no concrete validation set or code implementation.
Tags
Full text
# Do you have a validation set for Libor Market Model implementation? # Do you have a validation set for Libor Market Model implementation? 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? ## Answer by ctNGUYEN (score 2) https://quant.stackexchange.com/a/16174 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.
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