Abstract
We study American swaptions in the linear-rational (LR) term structure model introduced in Filipović et al. [J. Finance., 2017, 72, 655–704]. 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 Peskir [J. Theoret. Probab., 2005a, 18, 499–535]. We characterize the optimal stopping boundary as the unique solution to a non-linear 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.
Original language | British English |
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Pages (from-to) | 1865-1876 |
Number of pages | 12 |
Journal | Quantitative Finance |
Volume | 18 |
Issue number | 11 |
DOIs | |
State | Published - 2 Nov 2018 |
Keywords
- American swaption
- Free-boundary problem
- Integral equation
- Linear-rational term structure model
- Local time
- Optimal stopping
- Swap
- Swaption