The Lévy swap market model
نویسنده
چکیده
Models driven by Lévy processes are attractive since they allow for better statistical fitting compared to classical diffusion models. We derive the dynamics of the forward swap rate process in a semimartingale setting and introduce a Lévy swap market model. In order to guarantee positive rates, we model the swap rates as ordinary exponentials. We start with the most distant rate which is driven by a non-homogeneous Lévy process. Via backward induction we construct the remaining swap rates such that they become martingales under the corresponding forward swap measures. Finally we show how swaptions can be priced using bilateral Laplace transforms.
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