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Theory and Calibration of Swap Market Models

Galluccio, Stefano
Huang, Zhijhang
Ly, Jean-Michel
Year 2004
Collection Cahiers de recherche; 2004.01
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.
Keywords Swap market modelCapSwaptionCalibrationGraph Theory
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GALLUCCIO, Stefano et al. Theory and Calibration of Swap Market Models. 2004 https://archive-ouverte.unige.ch/unige:5781

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Deposited on : 2010-04-15

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