Theory and Calibration of Swap Market Models

Stefano Galluccio, Z. Huang, J.-M. Ly and Olivier Scaillet

FAME Research Paper Series from International Center for Financial Asset Management and Engineering

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.

Keywords: Swap Market Model; Cap; Swaption; Calibration; Graph Theory (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2005-06
New Economics Papers: this item is included in nep-cfn and nep-fin
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Related works:
Journal Article: THEORY AND CALIBRATION OF SWAP MARKET MODELS (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:fam:rpseri:rp107

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