On the American Swaption in the Linear-Rational Framework
Forthcoming, Quantitative Finance
26 Pages Posted: 8 Jul 2016 Last revised: 12 Mar 2018
Date Written: February 24, 2018
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: Suggested Citation