Market Models

The term structure models studied in preceding chapters involve assumptions about the evolution in one or more continuously compounded interest rates, either the short rate or the instantaneous forward rates. However, securities such as caps, floors, swaps, and swaptions depend on periodically compounded interest rates such as spot or forward LIBOR rates and spot or forward swap rates. For the pricing of these securities it seems appropriate to apply models that are based on assumptions on the LIBOR rates or the swap rates, and that is exactly what the market models do. LIBOR market models are based on assumptions on the evolution of the forward LIBOR rates, whereas swap market models are based on assumptions on the evolution of the forward swap rates. This chapter presents a general modelling framework, with special attention given to the so-called lognormal market models in which the derived prices for some caps or swaptions are consistent with the standard Black formula frequently applied by market practitioners. Alternative market models are also discussed.