Bonds Futures: Delta? No Gamma!

8 Pages Posted: 30 Jun 2006

See all articles by Marc P. A. Henrard

Marc P. A. Henrard

muRisQ Advisory; OpenGamma; University College London - Department of Mathematics

Date Written: May 2006

Abstract

Bond futures are liquid but complex instruments. Here they are analysed in a one-factor Gaussian HJM model. The in-the-model delta and out-of-the-model delta and gamma are studied. An explicit formula is provided for in-the-model delta. The out-of-the-model delta and gamma are equivalent to partial derivatives with respect to discount factors. In particular cases the derivative can not be obtained by standard techniques. The same situations lead to cases where the gammas (second order partial derivatives) do not exist.

Keywords: Bond future, delivery option, delta, gamma, HJM Gaussian model, in-the-model, out-of-the-model

JEL Classification: G13, E43

Suggested Citation

Henrard, Marc P. A., Bonds Futures: Delta? No Gamma! (May 2006). Available at SSRN: https://ssrn.com/abstract=912222 or http://dx.doi.org/10.2139/ssrn.912222

Marc P. A. Henrard (Contact Author)

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OpenGamma ( email )

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University College London - Department of Mathematics ( email )

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