Alternative Market Models

The BGM market model, examined in some detail in the previous chapter, is clearly oriented toward a particular interest rate, LIBOR, and thus it serves well for the valuation and hedging of the LIBOR related derivatives, such as plain-vanilla and exotic caps and floors. It thus may be see as a good candidate for the role of the Black-Scholes-like benchmark model for this particular sector of the fixed-income market. Interest rate swaps are another class of interest-rate-sensitive contracts of great practical importance. In a generic fixed-for-floating swap, a fixed rate of interest is exchanged periodically for some preassigned variable (floating) rate. Since swaps and derivative securities on the swap rate, termed swap derivatives, are in many markets more liquidly traded than LIBOR derivatives, there is an obvious demand for specific models capable of efficient handling this class of interest rate products. Our goal in this chapter is to present some recent research focused on market models that are alternatives to the market model for LIBORs.