In-Arrears Term Structure Products: No Arbitrage Pricing Bounds and the Convexity Adjustments

25 Pages Posted: 19 Oct 2009 Last revised: 16 Nov 2012

See all articles by Klaus Sandmann

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics

An Chen

University of Ulm

Date Written: October 16, 2009

Abstract

When pricing an in-arrears term structure product, the valuation usually boils down to determining the price of a vanilla product and of some additional part. To computer the price of the additional part, sometimes a specific term structure (like Gaussian or LIBOR) is assumed. Sometimes approximation methods are applied to achieve model-independent valuation formulae. In the present paper, we show that these valuation formulae (the price of vanilla products plus convexity adjustments resulting from approximation) are in effect model-independent pricing bounds in every arbitrage-free model. More specifically, they are proven to be a lower pricing bound for in-arrears payer swaps and in-arrears caps and an upper bound for in-arrears receiver swaps and in-arrears floors. To address the goodness/tightness issue of the bounds, convexity adjustments are compared with the exact pricing formulae obtained in LIBOR market model.

Keywords: In-arrears Swaps, In-arrears Caps and Floors, Convexity Adjustments, Pricing Bounds, Risk-neutral Pricing, Change of Measure.

JEL Classification: G12

Suggested Citation

Sandmann, Klaus and Chen, An, In-Arrears Term Structure Products: No Arbitrage Pricing Bounds and the Convexity Adjustments (October 16, 2009). International Journal of Theoretical and Applied Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1489945 or http://dx.doi.org/10.2139/ssrn.1489945

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics ( email )

Adenauerallee 24-26
Bonn, D-53113
Germany

An Chen (Contact Author)

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

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