On the American swaption in the linear-rational framework

TL;DR

This paper develops an analytical and numerical framework for pricing American swaptions within the linear-rational term structure model, providing explicit strategies and extending to Bermudan swaptions.

Contribution

It introduces a tractable approach to American swaption pricing using free-boundary problems and local time-space calculus within the LR model.

Findings

Explicit optimal exercise boundaries derived

Arbitrage-free American swaption prices computed

Efficient pricing method for Bermudan swaptions developed

Abstract

We study American swaptions in the linear-rational (LR) term structure model introduced in [5]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus of [7]. We characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation that can be readily solved numerically. We obtain the arbitrage-free price of the American swaption and the optimal exercise strategies in terms of swap rates for both fixed-rate payer and receiver swaps. Finally, we show that Bermudan swaptions can be efficiently priced as well.