Approximating the zero-coupon bond price in a general one-factor model with constant coefficients

TL;DR

This paper develops a recursive Taylor series expansion method for approximating zero-coupon bond prices in general one-factor short rate models with constant coefficients, providing a practical computational approach.

Contribution

It introduces a recursive formula for the Taylor expansion coefficients of bond prices, enabling efficient approximations in a broad class of one-factor models.

Findings

Series converge well in numerical examples

Method compares favorably with exact solutions in Cox-Ingersoll-Ross and Dothan models

Provides a practical tool for bond pricing in interest rate models

Abstract

We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around $\tau=0$, where $\tau$ is time to maturity. We provide numerical examples of convergence of the partial sums of the series and compare them with the known exact values in the case of Cox-Ingersoll-Ross and Dothan model.