Discount-Bond Derivatives on a Recombining Binomial Tree

Abstract

The "direct" approach to interest-rate derivatives, in which the fundamental quantity is a discount-bond price rather than an interest rate, is examined from a discrete-time viewpoint. A recombining binomial tree is constructed which reduces to the Buehler-Kaesler model in the continuous-time limit. Hopping probabilities and lattice spacings depend on the discount-bond value. The expiration value of the bond, at which the standard deviation and drift velocity vanish, is a limit point for tree sites; the limit point arises because, in the continuum model, the integral of the standard deviation's reciprocal diverges near the expiration price. Representative numerical results indicate that the binomial treatment yields a good approximation to the continuum results and that the approximation improves with the number of time steps. Applicability of the approach to other continuum models, e.g. Vasicek, is discussed.

JEL Classification: G13