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Theory and Calibration of Swap Market Models

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  • S.Galluccio

    ()

  • Z. Huang
  • J.-M. Ly
  • O. Scaillet

Abstract

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework, and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.

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Bibliographic Info

Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp107.

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Date of creation: Jun 2005
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Handle: RePEc:fam:rpseri:rp107

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Related research

Keywords: Swap Market Model; Cap; Swaption; Calibration; Graph Theory;

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Cited by:
  1. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
  2. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.

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