A Martingale Result for Convexity Adjustment in the Black Pricing Model
AbstractThis 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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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0212005.
Length: 118 pages
Date of creation: 21 Dec 2002
Date of revision:
Note: Type of Document - PDF; prepared on windows; pages: 118
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Martingale; Convexity Adjustment; Black and Black Scholes volatility; CMS rates.;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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- Jiří Witzany, 2009. "Valuation of Convexity Related Interest Rate Derivatives," Prague Economic Papers, University of Economics, Prague, vol. 2009(4), pages 309-326.
- 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.
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