The Libor Market Model (LMM) is an advanced mathematical model used to price interest rate derivatives. Also known as the BGM model after its authors (Brace, Gatarek, Musiela, 1997), the LMM has become hegemonic in the financial markets worldwide. The LMM in reality is not a single model, but rather as a large family of models (Rebonato 2000, Brigo and Mercurio, 2006). Its many variants include: the number of factors considered, the type of volatility modelling used, the type of correlation modelling used, if stochastic volatility or SABR are used, if forward libor rates or swap rates are used, if semi-analytical or numerical solution methods are used, among others. The many faces of the LMM offer the disadvantage of making it difficult to understand for beginners. It also makes it difficult to clearly see what is the best version to use in practice. Our aim in this contribution will be to construct the simplest possible version of the LMM, implement it in C++ and investigate its accuracy to price real market-quoted interest rate derivatives. We consider three examples: a plain vanilla interest rate swap (IRS), and IRS with a CAP and an IRS with a CORRIDOR feature. Our results show that in these cases our implementation of the LMM1F captures quite well the market prices of these products, as compared with Bloomberg and Sungard Monis.
The one factor libor market model using Monte Carlo simulation: an empirical investigation
PENA PINA, ALONSO;
2010
Abstract
The Libor Market Model (LMM) is an advanced mathematical model used to price interest rate derivatives. Also known as the BGM model after its authors (Brace, Gatarek, Musiela, 1997), the LMM has become hegemonic in the financial markets worldwide. The LMM in reality is not a single model, but rather as a large family of models (Rebonato 2000, Brigo and Mercurio, 2006). Its many variants include: the number of factors considered, the type of volatility modelling used, the type of correlation modelling used, if stochastic volatility or SABR are used, if forward libor rates or swap rates are used, if semi-analytical or numerical solution methods are used, among others. The many faces of the LMM offer the disadvantage of making it difficult to understand for beginners. It also makes it difficult to clearly see what is the best version to use in practice. Our aim in this contribution will be to construct the simplest possible version of the LMM, implement it in C++ and investigate its accuracy to price real market-quoted interest rate derivatives. We consider three examples: a plain vanilla interest rate swap (IRS), and IRS with a CAP and an IRS with a CORRIDOR feature. Our results show that in these cases our implementation of the LMM1F captures quite well the market prices of these products, as compared with Bloomberg and Sungard Monis.
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