LIBOR market model

Jarrow R, Li H, Zhao E (2004) Interest Rate Caps Smile Too But Can the LIBOR Market Model Capture It . Working paper, Cornell University. 

A drawback of the model is that it requires the input of instantaneous forward rates, which cannot necessarily be observed directly in the market. Models have been developed that are in the HIM approach that take this factor into account, including those presented by Brace et al. (1997) and Jamshidian (1997). This family of models is known as the LIBOR market model or the BGM model, fri the BGM model, there is initially one factor, the forward rate fit) which is the rate applicable from time to time t +i at time t. The forward rate is described by Equation (4.33) ... 

There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises. ... 

Jamshidian, F., 1997. LIBOR and swap market models and measures. Finance Stochast. 1,293-330. Jarrow, R., Madan, D., 1991. Option Pricing Using the Term Structure of Interest Rates to Hedge Systematic Discontinuities in Asset Returns Working Paper. Cornell University, Ithaca, NY,... 

The two previous chapters introduced and described a fractiOTi of the most important research into interest-rate models that has been carried out since the first model, presented by Oldrich Vasicek, appeared in 1977. These models can be used to price derivative seciuities, and equitibrium models can be used to assess fair value in the bond market. Before this can take place however, a model must be fitted to the yield curve, or calibrated In practice, this is carried out in two ways the most popular approach involves calibrating the model against market interest rates given by instruments such as cash Libor deposits, futures, swaps and bonds. The alternative method is to model the yield curve from the market rates and then calibrate the model to this fitted yield curve. The first approach is common when using, for example extended Vasicek... 

First, as mentioned earlier, there is usually no universal benchmark in a given market. Again, a possible approach, used in Barra s models, is to introduce a swap spread factor that describes the average spread between sovereign and swap rates and can conveniently allow spread risk to be expressed with respect to the LIBOR/swap curve when interest rate risk factors are originally based on the sovereign yield curve. 

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