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Pricing Swaptions And Coupon Bond Options In Affine Term Structure Models

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  • David F. Schrager
  • Antoon A. J. Pelsser

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.

Suggested Citation

  • David F. Schrager & Antoon A. J. Pelsser, 2006. "Pricing Swaptions And Coupon Bond Options In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 673-694, October.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:4:p:673-694
    DOI: 10.1111/j.1467-9965.2006.00289.x
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    References listed on IDEAS

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    Cited by:

    1. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 31, July-Dece.
    2. Vincenzo Russo & Gabriele Torri, 2019. "Calibration of one-factor and two-factor Hull–White models using swaptions," Computational Management Science, Springer, vol. 16(1), pages 275-295, February.
    3. João Pedro Vidal Nunes & Pedro Miguel Silva Prazeres, 2014. "Pricing Swaptions Under Multifactor Gaussian Hjm Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 762-789, October.
    4. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    5. Samson Assefa, 2007. "Calibration and Pricing in a Multi-Factor Quadratic Gaussian Model," Research Paper Series 197, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Malkhozov, Aytek & Mueller, Philippe & Vedolin, Andrea & Venter, Gyuri, 2013. "Mortgage hedging in fixed income markets," LSE Research Online Documents on Economics 119032, London School of Economics and Political Science, LSE Library.
    7. Date, Paresh & Wang, Chieh, 2009. "Linear Gaussian affine term structure models with unobservable factors: Calibration and yield forecasting," European Journal of Operational Research, Elsevier, vol. 195(1), pages 156-166, May.
    8. Frédéric Godin & Ramin Eghbalzadeh & Patrice Gaillardetz, 2023. "Pricing swaptions and zero-coupon futures options under the discrete-time arbitrage-free Nelson–Siegel model," Review of Derivatives Research, Springer, vol. 26(2), pages 171-206, October.
    9. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007.
    10. Plat, Richard & Pelsser, Antoon, 2009. "Analytical approximations for prices of swap rate dependent embedded options in insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 124-134, February.
    11. Leslie Ng, 2013. "Numerical Procedures For A Wrong Way Risk Model With Lognormal Hazard Rates And Gaussian Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-33.
    12. Aytek Malkhozov & Philippe Mueller & Andrea Vedolin & Gyuri Venter, 2013. "Mortgage Hedging in Fixed Income Markets," FMG Discussion Papers dp722, Financial Markets Group.
    13. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2132-2145, September.
    14. Marco Di Francesco & Roberta Simonella, 2023. "A stochastic Asset Liability Management model for life insurance companies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 61-94, March.
    15. Zorana Grbac & Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2014. "Affine LIBOR models with multiple curves: theory, examples and calibration," Papers 1405.2450, arXiv.org, revised Aug 2015.
    16. Abdelkoddousse Ahdida & Aur'elien Alfonsi & Ernesto Palidda, 2014. "Smile with the Gaussian term structure model," Papers 1412.7412, arXiv.org, revised Nov 2015.

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