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• W3125632163 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." @default.
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• W3125632163 date "2006-12-14" @default.
• W3125632163 modified "2023-10-12" @default.
• W3125632163 title "THEORY AND CALIBRATION OF SWAP MARKET MODELS" @default.
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• W3125632163 doi "https://doi.org/10.1111/j.1467-9965.2007.00296.x" @default.
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