PRICING SWAPTIONS AND COUPON BOND OPTIONS IN AFFINE TERM STRUCTURE MODELS

Authors: Schrager, DavidF.¹; Pelsser, AntoonA. J.²

Source: Mathematical Finance, Volume 16, Number 4, October 2005 , pp. 673-694(22)

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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.

Keywords: swaption; coupon bond option; affine term structure models; change of numéraire; swap measure; conditional characteristic function; option pricing using transform inversion

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9965.2006.00289.x

Affiliations: 1: ING and University of Amsterdam 2: University of Amsterdam and ING

Publication date: 2005-10-01