A Levy HJM Multiple-Curve Model with Application to CVA Computation

29 Pages Posted: 2 Oct 2013

See all articles by Stéphane Crépey

Stéphane Crépey

Université d'Évry - Equipe d'Analyse et Probabilites

Zorana Grbac

Université Paris VII Denis Diderot

Nathalie Ngor

Université d'Évry

David Skovmand

Aarhus University - School of Business and Social Sciences

Date Written: September 25, 2013

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 Levy process. We proceed with joint calibration to caps and swaptions of different tenors, the calibration to caps guaranteeing that the model correctly captures volatility smile e ffects (in strike) and the calibration to at-the-money swaptions ensuring an appropriate term structure of the volatility in the model. To account for counter-party 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 counter-party 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, for which we compute the counter-party risk and funding adjustments.

Keywords: interest rate derivative, multiple-curve term structure model, Levy process, credit valuation adjustment (CVA), funding

JEL Classification: G12, E43

Suggested Citation

Crépey, Stéphane and Grbac, Zorana and Ngor, Nathalie and Skovmand, David, A Levy HJM Multiple-Curve Model with Application to CVA Computation (September 25, 2013). Available at SSRN: https://ssrn.com/abstract=2334865 or http://dx.doi.org/10.2139/ssrn.2334865

Stéphane Crépey (Contact Author)

Université d'Évry - Equipe d'Analyse et Probabilites ( email )

Boulevard des Coquibus
F-91025 Evry Cedex
France

Zorana Grbac

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Nathalie Ngor

Université d'Évry ( email )

Bd. François Mitterrand
F-91025 Evry Cedex, 91028
France

David Skovmand

Aarhus University - School of Business and Social Sciences ( email )

Nordre Ringgade 1
Aarhus C, DK-8000
Denmark

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