Theory and Calibration of Swap Market Models

31 Pages Posted: 13 Dec 2006

See all articles by Stefano Galluccio

Stefano Galluccio

BNP Paribas Fixed Income

Jean-Michel Ly

BNP Paribas Fixed Income

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics

Z. Huang

JP Morgan

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Abstract

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of forward 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.

Suggested Citation

Galluccio, Stefano and Ly, Jean-Michel and Scaillet, Olivier and Huang, Z., Theory and Calibration of Swap Market Models. Mathematical Finance, Vol. 17, No. 1, pp. 111-141, January 2007, Available at SSRN: https://ssrn.com/abstract=951333 or http://dx.doi.org/10.1111/j.1467-9965.2007.00296.x

Stefano Galluccio (Contact Author)

BNP Paribas Fixed Income ( email )

10, Harewood Avenue
NW1 6AA London
United Kingdom

Jean-Michel Ly

BNP Paribas Fixed Income ( email )

10 Harewood Avenue
NW1 6AA London
United Kingdom

Olivier Scaillet

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland
+ 41 22 379 88 16 (Phone)
+41 22 389 81 04 (Fax)

HOME PAGE: http://www.scaillet.ch

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva - Research Center for Statistics

Geneva
Switzerland

Z. Huang

JP Morgan

London
United Kingdom

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