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A Martingale Result for Convexity Adjustment in the Black Pricing Model

LSE Working Paper

18 Pages Posted: 27 Apr 2001  

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil

Date Written: May 2000

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 approximation, we come to a closed formula with specification 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

JEL Classification: G12, G13

Suggested Citation

Benhamou, Eric, A Martingale Result for Convexity Adjustment in the Black Pricing Model (May 2000). LSE Working Paper. Available at SSRN: https://ssrn.com/abstract=265276 or http://dx.doi.org/10.2139/ssrn.265276

Eric Benhamou (Contact Author)

Université Paris Est - Université Paris Est-Creteil ( email )

61 avenue du Général de Gaulle
Créteil, 940000
France

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