A closed-form formula for pricing bonds between coupon payments

TL;DR

This paper presents a closed-form formula for bond pricing between coupon payments, applicable to both Treasury and Street methods, enabling quick and resource-efficient calculation of bond prices at any date.

Contribution

The authors derive a novel closed-form formula that simplifies bond pricing between coupon dates for various pricing methods, reducing computational effort.

Findings

Accurately priced UK gilts at any date using the formula

Reduced computational resources needed for bond valuation

Validated the formula with real bond data

Abstract

We derive a closed-form formula for computing bond prices between coupon payments. Our results cover both the `Treasury' and the `Street' pricing methods used by sovereign and corporate issuers. We apply our formulas to two UK gilts, the 8% Treasury Gilt 2015, and the 0.5% Treasury Gilt 2022, and show that we can obtain the dirty price of these bonds at any date with a minimum of calculations, and without intensive computational resources.