• Financial support by FCT's grant number PTDC/EGE-ECO/099255/2008 is gratefully acknowledged. The authors also thank the co-editor and two anonymous referees, whose corrections have significantly improved this paper.

  • The analyses, opinions, and findings of this paper represent the views of the authors, and they are not necessarily those of the Sociedade Gestora dos Fundos de Pensões do Banco de Portugal, the Banco de Portugal, or the Eurosystem.


Several approximations have been proposed in the literature for the pricing of European-style swaptions under multifactor term structure models. However, none of them provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique of Collin-Dufresne and Goldstein is able to characterize the order of the approximation error. Under a multifactor HJM Gaussian framework, this paper proposes a new approximation for European-style swaptions, which is able to set bounds on the magnitude of the approximation error and is based on the conditioning approach initiated by Curran and Rogers and Shi. All the proposed pricing bounds will arise as a simple by-product of the Nielsen and Sandmann setup, and will be shown to provide a better accuracy–efficiency trade-off than all the approximations already proposed in the literature.