LIBOR and Swap Market Models

Abstract A number of models have been successfully developed wherein the theoretical prices for caps, floors, and swaptions produced by the model are of the Black-76 form. In these models, discrete market rates are modelled like LIBOR rates in the LIBOR market models or forward swap rates in the swap market models; and under a suitable choice of numeraires, market rates can be modelled log normally. LIBOR caps and the market practice for pricing and quoting these instruments are discussed. It is shown that given a swap market model, the LIBOR rates will not be lognormal; thus, LIBOR market models and swap models are generally incompatible. Practice exercises are included.