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A Martingale Result for Convexity Adjustment in the Black Pricing Model

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Author Info

  • Eric Benhamou

    (Goldman Sachs International)

Abstract

This paper explains how to calculate convexity adjustment for interest rates derivatives when assuming a deterministic time dependent volatility, using martingale theory. The motivation of this paper lies in two directions. First, we set up a proper no-arbitrage framework illustrated by a relationship between yield rate drift and bond price. Second, making ap-proximation, we come to a closed formula with speci…cation of the error term. Earlier works (Brotherton et al. (1993) and Hull (1997)) assumed constant volatility and could not specify the approximation error. As an application, we examine the convexity bias between CMS and forward swap rates.

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File URL: http://128.118.178.162/eps/fin/papers/0212/0212005.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0212005.

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Length: 118 pages
Date of creation: 21 Dec 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0212005

Note: Type of Document - PDF; prepared on windows; pages: 118
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Web page: http://128.118.178.162

Related research

Keywords: Martingale; Convexity Adjustment; Black and Black Scholes volatility; CMS rates.;

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References

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  1. French, Kenneth R., 1983. "A comparison of futures and forward prices," Journal of Financial Economics, Elsevier, vol. 12(3), pages 311-342, November.
  2. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  3. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  4. Eric Benhamou, 2000. "Pricing Convexity Adjustment with Wiener Chaos," FMG Discussion Papers dp351, Financial Markets Group.
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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Cited by:
  1. Didier Kouokap Youmbi, 2012. "Yield to maturity modelling and a Monte Carlo Technique for pricing Derivatives on Constant Maturity Treasury (CMT) and Derivatives on forward Bonds," Papers 1204.4631, arXiv.org.
  2. Jiří Witzany, 2009. "Valuation of Convexity Related Interest Rate Derivatives," Prague Economic Papers, University of Economics, Prague, vol. 2009(4), pages 309-326.
  3. A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.

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