Theory and Calibration of Swap Market Models
AbstractThis 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 InfoPaper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp107.
Date of creation: Jun 2005
Date of revision:
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Swap Market Model; Cap; Swaption; Calibration; Graph Theory;
Other versions of this item:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-06-13 (All new papers)
- NEP-CFN-2004-06-13 (Corporate Finance)
- NEP-FIN-2004-06-13 (Finance)
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