On the American Swaption in the Linear-Rational Framework

Forthcoming, Quantitative Finance

Swiss Finance Institute Research Paper No. 16-44

26 Pages Posted: 8 Jul 2016 Last revised: 12 Mar 2018

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Yerkin Kitapbayev

North Carolina State University

Date Written: February 24, 2018

Abstract

We study American swaptions in the linear-rational (LR) term structure model introduced. 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. 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.

Keywords: American swaption, swaption, swap, linear-rational term structure model, polynomial diffusion, optimal stopping, free-boundary problem, local time-space calculus, integral equation

JEL Classification: G12, G13

Suggested Citation

Filipovic, Damir and Kitapbayev, Yerkin, On the American Swaption in the Linear-Rational Framework (February 24, 2018). Forthcoming, Quantitative Finance; Swiss Finance Institute Research Paper No. 16-44. Available at SSRN: https://ssrn.com/abstract=2806119 or http://dx.doi.org/10.2139/ssrn.2806119

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Yerkin Kitapbayev

North Carolina State University ( email )

Hillsborough Street
Raleigh, NC 27695
United States

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