Fast and accurate analytical approximation of bond prices when short interest rates are lognormal

Abstract

The authors present an analytical approximation formula for zero-coupon bond prices in a one-factor term structure model where the short interest rate follows a lognormal diffusion. An analytical bound on the error is also derived and is used to show that the pricing formula is virtually exact for a wide range of parameter values. The pricing formula is easily implemented and is extremely fast. Illustrative numerical examples are provided and comparisons with results from implementation of the standard binomial model are made. The comparisons support the effectiveness of the proposed algorithm.