On the American swaption in the linear-rational framework

2016/07/07 by Damir Filipovic, Filipovic, Damir, Yerkin Kitapbayev +1
Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #q-fin.MF #q-fin.PR

paper · pdf · doi:10.48550/arxiv.1607.02067

forthcoming in Quantitative Finance, 2018

arxiv created 2018/02/24 · arxiv updated 2018/02/27

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.

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