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In-Arrears Term Structure Products: No Arbitrage Pricing Bounds And The Convexity Adjustments

Author

Listed:
  • AN CHEN

    (Department of Mathematics and Economics, University of Ulm, Helmholtzstrasse 20, 89069 Ulm, Germany)

  • KLAUS SANDMANN

    (Department of Economics, University of Bonn, Adenauerallee 24-42, 53113 Bonn, Germany)

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.

Suggested Citation

  • An Chen & Klaus Sandmann, 2012. "In-Arrears Term Structure Products: No Arbitrage Pricing Bounds And The Convexity Adjustments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-24.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:08:n:s0219024912500549
    DOI: 10.1142/S0219024912500549
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