THEORY AND CALIBRATION OF SWAP MARKET MODELS

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

Mathematical Finance, 2007, vol. 17, issue 1, 111-141

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.

Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9965.2007.00296.x

Related works:
Working Paper: Theory and Calibration of Swap Market Models (2005)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:17:y:2007:i:1:p:111-141

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0960-1627

Access Statistics for this article

Mathematical Finance is currently edited by Jerome Detemple

More articles in Mathematical Finance from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().