The Construction of a Path-Independent Interest Rate Tree: The Model of Heath, Jarrow and Morton

Abstract

Recently, Heath, Jarrow, and Morton (1987) made an important contribution to the valuation of interest rate-derivative securities. They extended the model of Ho and Lee (1986) by allowing for several stochastically independent movements of the exogenous term structure. Besides this, they derived the risk-neutral description of the forward-rate process, which facilitates estimation of the volatility parameters. A serious disadvantage, however, is the proposed numerical method for the construction of an interest rate tree. The approach they suggested will result in a tree that is path dependent. This paper develops an alternative algorithm for the construction of an interest rate tree that is path independent. In addition, an extension is derived to obtain the different sensitivities of any contingent claim with regard to the stochastic movements of the term structure. Numerical examples show the efficiency of the procedure described.

JEL Classification: G13, E43