Models of Bond Prices and LIBOR Rates

Abstract

The Heath-Jarrow-Morton methodology of term structure modelling presented in the previous chapter is based on the arbitrage-free dynamics of instantaneous, continuously compounded forward rates. The assumption that instantaneous rates exist is not always convenient, since it requires some degree of smoothness with respect to the tenor (i.e., maturity) of bond prices and their volatilities. An alternative construction of an arbitrage-free family of bond prices, making no reference to the instantaneous, continuously compounded rates, is in some circumstances more suitable. The first step in this direction was taken by Sandmann and Sondermann (1994), who focused on the effective annual interest rate (cf. Sect. 12.3.2). This idea was further developed by Goldys et al. (1994), Musiela (1994), Sandmann et al. (1995), Miltersen et al. (1997) and Brace et al. (1997).