Approximations of Bond and Swaption Prices in a Black-Karasi\'{n}ski Model

TL;DR

This paper introduces semi-analytic approximation formulas for bond and swaption prices within a Black-Karasiński interest rate model, utilizing a novel Karhunen-Loève expansion technique for efficient and accurate computations.

Contribution

It presents a new approximation method based on Karhunen-Loève expansion that enhances computational efficiency and accuracy for pricing in the Black-Karasiński model.

Findings

Formulas are easily computable.

Approximations are highly accurate in numerical tests.

Useful for efficient model calibration.

Abstract

We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasi\'{n}ski interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Lo\`{e}ve expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for numerically efficient calibration of the model.