Henrard, Marc (2006): Bonds futures: Delta? No gamma!

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Abstract
Bond futures are liquid but complex instruments. Here they are analysed in a onefactor Gaussian HJM model. The inthemodel delta and outofthemodel delta and gamma are studied. An explicit formula is provided for inthemodel delta. The outofthemodel 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 exists.
Item Type:  MPRA Paper 

Institution:  BIS 
Original Title:  Bonds futures: Delta? No gamma! 
Language:  English 
Keywords:  Bond future; delivery option; delta; gamma; HJM gaussian model; inthemodel; outofthemodel 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E43  Interest Rates: Determination, Term Structure, and Effects 
Item ID:  2249 
Depositing User:  Marc Henrard 
Date Deposited:  14. Mar 2007 
Last Modified:  20. Feb 2013 18:33 
References:  Brody, D.~C. and Hughston, L.~P. (2004). Chaos and coherence: a new framework for interestrate modelling. Proc. R. Soc. Lond. A., 460:85110. Carverhill, A. (1994). When is the short rate Markovian. Mathematical Finance, 4(4):305312. Heath, D., Jarrow, R., and Morton, A. (1992). Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica, 60(1):77105. Henrard, M. (2003). Explicit bond option and swaption formula in HeathJarrowMorton onefactor model. International Journal of Theoretical and Applied Finance, 6(1):5772. Henrard, M. (2006a). Bonds futures and their options: more than the cheapesttodeliver; quality option and marginning. Technical report, SSRN. Henrard, M. (2006b). A semiexplicit approach to Canary swaptions in HJM onefactor model. Applied Mathematical Finance, 13(1):118. Hunt, P.~J. and Kennedy, J.~E. (2004). Financial Derivatives in Theory and Practice. Wiley series in probability and statistics. Wiley, second edition. Lamberton, D. and Lapeyre, B. (2000). Introduction to stochastic calculus applied to finance. Capman \& Hall / CRC. Nunes, J. and de~Oliveira, L. (2004). Quasianalytical multifactor valuation of treasury bond futures with and embedded quality option. Technical Report 2493, EFA 2004 Maastricht Meeting. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/2249 