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

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 y...

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Bibliographic Details
Published in:IDEAS Working Paper Series from RePEc 2017-04, Vol.24 (3), p.29-41
Main Authors: Leblon, Grégoire, Moraux, Franck
Format: Article
Language:English
Subjects:
Business administration
Econometrics
Economic models
Economics and Finance
Fourier transforms
Humanities and Social Sciences
Interest rates
Ordinary differential equations
Prices
Probability
Put & call options
Yield to maturity
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Summary: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.
ISSN:1074-1240
2168-8524
DOI:10.3905/jod.2017.24.3.029