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Funding, repo and credit inclusive valuation as modified option pricing

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  • Damiano Brigo
  • Cristin Buescu
  • Marek Rutkowski

Abstract

We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark vulnerable claim there is an analytical solution, and we express it in terms of the Black-Scholes formula with dividends. This allows for a detailed valuation analysis, stress testing and risk analysis via sensitivities.

Suggested Citation

  • Damiano Brigo & Cristin Buescu & Marek Rutkowski, 2016. "Funding, repo and credit inclusive valuation as modified option pricing," Papers 1602.05998, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1602.05998
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    References listed on IDEAS

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    1. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2011. "Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation," Papers 1112.1521, arXiv.org, revised Dec 2011.
    2. Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2015. "Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs," Papers 1506.00686, arXiv.org, revised Nov 2015.
    3. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
    4. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    5. Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2005. "PDE approach to valuation and hedging of credit derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 257-270.
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    Cited by:

    1. Contessi, Silvio & De Pace, Pierangelo & Guidolin, Massimo, 2020. "Mildly explosive dynamics in U.S. fixed income markets," European Journal of Operational Research, Elsevier, vol. 287(2), pages 712-724.
    2. F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "CVA and vulnerable options pricing by correlation expansions," Annals of Operations Research, Springer, vol. 299(1), pages 401-427, April.
    3. Junbeom Lee & Chao Zhou, 2021. "Binary funding impacts in derivative valuation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 242-278, January.
    4. Tumasyan, Hovik, 2018. "A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral," MPRA Paper 90806, University Library of Munich, Germany.
    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. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228, arXiv.org.
    7. Junbeom Lee & Chao Zhou, 2017. "Binary Funding Impacts in Derivative Valuation," Papers 1703.00259, arXiv.org, revised Aug 2020.
    8. Hovik Tumasyan, 2018. "A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral," Papers 1806.09198, arXiv.org, revised Dec 2018.

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