IN-ARREARS TERM STRUCTURE PRODUCTS: NO ARBITRAGE PRICING BOUNDS AND THE CONVEXITY ADJUSTMENTS

An Chen () and Klaus Sandmann
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An Chen: Department of Mathematics and Economics, University of Ulm, Helmholtzstrasse 20, 89069 Ulm, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2012, vol. 15, issue 08, 1-24

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 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0219024912500549

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