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Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

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  • Brigo, Damiano
  • Francischello, Marco
  • Pallavicini, Andrea

Abstract

Since the 2008 global financial crisis, the banking industry has been using valuation adjustments to account for default risk and funding costs. These adjustments are computed separately and added together by practitioners as if the valuation equations were linear. This assumption is too strong and does not allow to model market features such as different borrowing and lending rates and replacement default closeout. Hence we argue that the full valuation equations are nonlinear, and this paper is devoted to studying the nonlinear valuation equations introduced in Pallavicini et al (2011).

Suggested Citation

  • Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
    • Handle: RePEc:eee:ejores:v:274:y:2019:i:2:p:788-805
    DOI: 10.1016/j.ejor.2018.10.046
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    References listed on IDEAS

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    Cited by:

    1. Francesca Biagini & Alessandro Gnoatto & Immacolata Oliva, 2019. "Pricing of counterparty risk and funding with CSA discounting, portfolio effects and initial margin," Working Papers 04/2019, University of Verona, Department of Economics.
    2. van der Zwaard, Thomas & Grzelak, Lech A. & Oosterlee, Cornelis W., 2022. "Relevance of Wrong-Way Risk in Funding Valuation Adjustments," Finance Research Letters, Elsevier, vol. 49(C).
    3. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    4. Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2022. "Approximate value adjustments for European claims," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1149-1161.
    5. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2022. "Nonlinear Valuation with XVAs: Two Converging Approaches," Mathematics, MDPI, vol. 10(5), pages 1-31, March.
    6. Alessio Calvelli, 2022. "No-Arbitrage Pricing, Dynamics and Forward Prices of Collateralized Derivatives," Papers 2208.08746, arXiv.org, revised Jun 2024.
    7. Joel P. Villarino & 'Alvaro Leitao & Jos'e A. Garc'ia-Rodr'iguez, 2022. "Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk," Papers 2210.02175, arXiv.org.
    8. Kazuhiro Takino, 2022. "The impact of non-cash collateralization on the over-the-counter derivatives markets," Review of Derivatives Research, Springer, vol. 25(2), pages 137-171, July.
    9. Damiano Brigo & Federico Graceffa & Alexander Kalinin, 2021. "Mild to classical solutions for XVA equations under stochastic volatility," Papers 2112.11808, arXiv.org.
    10. Chaofan Sun & Ken Seng Tan & Wei Wei, 2022. "Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms," Papers 2201.09105, arXiv.org, revised Jan 2022.

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