LIBOR Market Model (LMM) class creation using historical spot rates

I am creating an LMM class and I am following the example given in the documentation page. (http://www.mathworks.com/help/fininst/libormarketmodel-class.html)

I notice there are variables such as LMMVolFunc, LMMVolParams, Beta etc. that have been defined. How are these defined and where do the definitions come from?

I have a history of spot rates. Is it possible that I can define the LMMVolFunc using that? If so how?

Answer 1

[MathWorks Support Team]

The volatilities and correlations for the LMM are calibrated either using the market data (such as swaptions, caps, and floors) or using the historical data (like the spot rate history that you have).

While we currently have an example in the documentation to illustrate the procedure to calibrate to market data, we do not have an example showing how to calibrate the model to historical data. You can find out how to calibrate to market data using the following documentation link :

https://www.mathworks.com/help/fininst/price-bermudan-swaptions-with-different-interest-rate-models.html

For more information on historical calibration and different parameterizations for the volatilities and correlation, the following references would be helpful : 

“Interest Rate Models - Theory and Practice” by Brigo and Mercurio

https://books.google.com/books?id=C31l_fs-mMkC

 

“Interest Rate Modeling” by Andersen and Piterbarg

https://books.google.com/books?id=oI2fcQAACAAJ

 

The "LMMVolFunc", "LMMVolParams", "Beta", and "CorrFunc" variables in the documentation page are set from these sources.