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A L�vy HJM multiple-curve model with application to CVA computation

Author

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  • St�phane Cr�pey
  • 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 L�vy 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

  • St�phane Cr�pey & Zorana Grbac & Nathalie Ngor & David Skovmand, 2015. "A L�vy 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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    Citations

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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. Alessandro Gnoatto & Nicole Seiffert, 2020. "Cross Currency Valuation and Hedging in the Multiple Curve Framework," Papers 2001.11012, arXiv.org, revised Mar 2021.
    3. Atkins, Philip J. & Cummins, Mark, 2023. "Improved scalability and risk factor proxying with a two-step principal component analysis for multi-curve modelling," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1331-1348.
    4. Ming-Chieh Wang & Li-Jhang Huang, 2019. "Pricing cross-currency interest rate swaps under the Levy market model," Review of Derivatives Research, Springer, vol. 22(2), pages 329-355, July.
    5. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    6. 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.
    7. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    8. Yangfan Zhong & Yanhui Mi, 2018. "Pricing in-arrears caps and ratchet caps under LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-31, September.
    9. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    10. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    11. Fanelli, Viviana, 2017. "Implications of implicit credit spread volatilities on interest rate modelling," European Journal of Operational Research, Elsevier, vol. 263(2), pages 707-718.
    12. Markus Hess, 2020. "A pure-jump mean-reverting short rate model," Papers 2006.14814, arXiv.org.
    13. Yangfan Zhong, 2018. "LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-38, June.
    14. Nikolaos Karouzakis & John Hatgioannides & Kostas Andriosopoulos, 2018. "Convexity adjustment for constant maturity swaps in a multi-curve framework," Annals of Operations Research, Springer, vol. 266(1), pages 159-181, July.

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