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PRICING SWAPTIONS AND COUPON BOND OPTIONS IN AFFINE TERM STRUCTURE MODELS

Authors


  • The authors would like to thank Peter Boswijk, Frank de Jong, and participants at the Bachelier Congress in Chicago for discussion and comments. The comments of an anonymous referee are acknowledged.

  • Manuscript received October 2004; final revision received August 2005.

Address correspondence to David F. Schrager, Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands; e-mail: david.schrager@mail.ing.nl.

Abstract

We propose an approach to find an approximate price of a swaption in affine term structure models. Our approach is based on the derivation of approximate swap rate dynamics in which the volatility of the forward swap rate is itself an affine function of the factors. Hence, we remain in the affine framework and well-known results on transforms and transform inversion can be used to obtain swaption prices in similar fashion to zero bond options (i.e., caplets). The method can easily be generalized to price options on coupon bonds. Computational times compare favorably with other approximation methods. Numerical results on the quality of the approximation are excellent. Our results show that in affine models, analogously to the LIBOR market model, LIBOR and swap rates are driven by approximately the same type of (in this case affine) dynamics.

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