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A Lévy HJM multiple-curve model with application to CVA computation

Abstract : We consider the problem of valuation of interest rate derivatives in the post-crisis setup. We develop a multiple-curve model, set in the HJM framework and driven by a L ́evy process. We proceed with joint calibration to OTM swaptions and co-terminal ATM swaptions of different tenors, the calibration to OTM swaptions guaranteeing that the model correctly captures volatility smile effects and the calibration to co-terminal ATM swaptions ensuring an appropriate term structure of the volatility in the model. To account for counterparty risk and funding issues, we use the calibrated multiple- curve model as an underlying model for CVA computation. We follow a reduced-form methodology through which the problem of pricing the counterparty risk and funding costs can be reduced to a pre-default Markovian BSDE, or an equivalent semi-linear PDE. As an illustration we study the case of a basis swap and a related swaption, for which we compute the counterparty risk and funding adjustments.
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https://hal.archives-ouvertes.fr/hal-01485698
Contributor : Serena Benassù <>
Submitted on : Thursday, March 9, 2017 - 12:14:06 PM
Last modification on : Friday, March 27, 2020 - 3:54:00 AM

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  • HAL Id : hal-01485698, version 1

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Zorana Grbac, Stéphane Crépey, Nathalie Ngor, David Skovmand. A Lévy HJM multiple-curve model with application to CVA computation . Quantitative Finance, Taylor & Francis (Routledge), 2015, 15 (3), pp.401-419. ⟨hal-01485698⟩

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