We are grateful for financial support from the Gifford Fong Associates Fund, at the Graduate School of Business, Stanford University.
PRICING COUPON-BOND OPTIONS AND SWAPTIONS IN AFFINE TERM STRUCTURE MODELS
Article first published online: 8 JAN 2007
Volume 12, Issue 4, pages 427–446, October 2002
How to Cite
Singleton, K. J. and Umantsev, L. (2002), PRICING COUPON-BOND OPTIONS AND SWAPTIONS IN AFFINE TERM STRUCTURE MODELS. Mathematical Finance, 12: 427–446. doi: 10.1111/j.1467-9965.2002.tb00132.x
- Issue published online: 8 JAN 2007
- Article first published online: 8 JAN 2007
- Manuscript received April 2001; final revision received February 2002.
- Coupon-bond options;
- affine term structure model;
- expected exposure
This paper provides a numerically accurate and computationally fast approximation to the prices of European options on coupon-bearing instruments that is applicable to the entire family of affine term structure models. Exploiting the typical shapes of the conditional distributions of the risk factors in affine diffusions, we show that one can reliably compute the relevant probabilities needed for pricing options on coupon-bearing instruments by the same Fourier inversion methods used in the pricing of options on zero-coupon bonds. We apply our theoretical results to the pricing of options on coupon bonds and swaptions, and the calculation of “expected exposures” on swap books. As an empirical illustration, we compute the expected exposures implied by several affine term structure models fit to historical swap yields.