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Article

Analytical Pricing of European Bond Options within One-Factor Quadratic Term Structure Models

Grégoire Leblon and Franck Moraux
The Journal of Derivatives Spring 2017, 24 (3) 29-41; DOI: https://doi.org/10.3905/jod.2017.24.3.029
Grégoire Leblon
is a quantitative researcher in a London-based hedge fund and an associate fellow at Centre de Recherche en Économie et Management in Rennes, France.
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  • For correspondence: gregoire.leblon@gmail.com
Franck Moraux
is a professor at the Université de Rennes 1 and Centre de Recherche en Économie et Management in Rennes, France.
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  • For correspondence: franck.moraux@univ-rennes1.fr
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Abstract

Jamshidian developed a model for pricing bond options within a Vasicek one-factor framework, with the very useful property that it allows an option on a coupon bond to be decomposed into a set of options on the individual coupons. In the Vasicek framework, the “Jamshidian trick” produces yields to maturity on the coupons that are linear functions of the underlying state variable. But it has not been clear whether this approach could extend to more complicated interest rate processes. In this article, Leblon and Moraux show how to extend the Jamshidian technique to quadratic interest rate processes and use it to derive analytic formulas for European call options on coupon bonds. Finally, they verify that the required conditions appear to hold in the real world.

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The Journal of Derivatives: 24 (3)
The Journal of Derivatives
Vol. 24, Issue 3
Spring 2017
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Analytical Pricing of European Bond Options within One-Factor Quadratic Term Structure Models
Grégoire Leblon, Franck Moraux
The Journal of Derivatives Feb 2017, 24 (3) 29-41; DOI: 10.3905/jod.2017.24.3.029

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Analytical Pricing of European Bond Options within One-Factor Quadratic Term Structure Models
Grégoire Leblon, Franck Moraux
The Journal of Derivatives Feb 2017, 24 (3) 29-41; DOI: 10.3905/jod.2017.24.3.029
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  • Article
    • Abstract
    • THE FRAMEWORK
    • THE DISCOUNT BOND OPTION CASE
    • THE COUPON BOND OPTION CASE
    • DISCUSSION OF THE JAMSHIDIAN TRICK AS APPLIED TO ONE-FACTOR QTSMS
    • CONCLUSION
    • APPENDIX A
    • APPENDIX B
    • APPENDIX C
    • APPENDIX D
    • APPENDIX E
    • APPENDIX F
    • APPENDIX G
    • APPENDIX H
    • APPENDIX I
    • ENDNOTES
    • REFERENCES
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