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

Author

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  • Stéphane Crépey
  • Zorana Grbac
  • Nathalie Ngor
  • David Skovmand

Abstract

We consider the problem of valuation of interest rate derivatives in the post-crisis set-up. We develop a multiple-curve model, set in the HJM framework and driven by a Lévy 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.

Suggested Citation

  • Stéphane Crépey & Zorana Grbac & Nathalie Ngor & David Skovmand, 2015. "A Lévy HJM multiple-curve model with application to CVA computation," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 401-419, March.
  • Handle: RePEc:taf:quantf:v:15:y:2015:i:3:p:401-419
    DOI: 10.1080/14697688.2014.942232
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    File URL: http://hdl.handle.net/10.1080/14697688.2014.942232
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    Cited by:

    1. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    2. repec:eee:ejores:v:263:y:2017:i:2:p:707-718 is not listed on IDEAS
    3. repec:wsi:ijfexx:v:05:y:2018:i:02:n:s2424786318500147 is not listed on IDEAS
    4. The Anh Nguyen & Frank Thomas Seifried, 2015. "The Multi-Curve Potential Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-32, November.
    5. repec:spr:annopr:v:266:y:2018:i:1:d:10.1007_s10479-017-2430-6 is not listed on IDEAS
    6. repec:wsi:ijfexx:v:05:y:2018:i:03:n:s2424786318500238 is not listed on IDEAS

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