10.6 Conclusion

This model is the first to allow a direct matching of the initial observed term structure. The model contrasts to previously developed models by considering the stochastic development of the whole term structure. Hence, each node in the binomial tree has a series of discount bond prices (or equivalently, rates of interest) of various maturities associated with it. This contrasts to, say, the BDT model (Chapter 8) where at each node, one only considers the value of the short- term interest rate applicable over the next time step.

Models such as the Vasicek [ 50 ] and CIR [ 18 ] models hypothesise a functional form for the stochastic process governing the evolution of the short- term interest rate. They then attempt to determine parameter values so as to match, as closely as possible, the market-observed term structure. HL use a different approach by using the market-observed term structure to specify the stochastic process of the short-term interest rate. This allows all securities to be priced relative to the observed term structure.