Bonds futures and their options: more than the cheapest-to-deliver; quality option and marginning
Even if the name futures indicates a simple instrument, bond futures are complex. Several special features are embedded in the instrument. In particular the future is not written on one specific bond but on a basket of bonds, from which the short side can deliver the cheapest. This paper focuses on that feature, present in the main futures market, and its impact on the futures risk. A formula for the delivery option and the convexity adjustment due to the daily margining is proposed in the Gaussian HJM model. The approach is numerically very efficient and easy to implement. Based on this result a futures option formula is derived. The approach is similar to the one used for Canary swaptions.
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- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Henrard, Marc, 2006. "Bonds futures: Delta? No gamma!," MPRA Paper 2249, University Library of Munich, Germany, revised 01 May 2006.
- Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, EconWPA.
- Marc Henrard, 2006. "A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 1-18.
- Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, EconWPA, revised 14 Aug 2004.
- Bing-Huei Lin & Ren-Raw Chen & Jian-Hsin Chou, 1999. "Pricing and quality option in Japanese government bond futures," Applied Financial Economics, Taylor & Francis Journals, vol. 9(1), pages 51-65.
- Marc Henrard, 2004. "Semi-explicit Delta and Gamma for European swaptions in Hull- White one factor model," Finance 0411036, EconWPA, revised 25 Jan 2005.
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