IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.05998.html
   My bibliography  Save this paper

Funding, repo and credit inclusive valuation as modified option pricing

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.05998
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Junbeom Lee & Chao Zhou, 2017. "Binary Funding Impacts in Derivative Valuation," Papers 1703.00259, arXiv.org, revised Aug 2020.
    7. Junbeom Lee & Chao Zhou, 2021. "Binary funding impacts in derivative valuation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 242-278, January.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2016. "Arbitrage-Free XVA," Papers 1608.02690, arXiv.org.
    5. Han, Xingyu, 2018. "Pricing and hedging vulnerable option with funding costs and collateral," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 103-115.
    6. 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.
    7. Meng Han & Yeqi He & Hu Zhang, 2014. "A note on discounting and funding value adjustments for derivatives," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-34.
    8. Damiano Brigo & Qing Liu & Andrea Pallavicini & David Sloth, 2014. "Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes," Papers 1404.7314, arXiv.org.
    9. Yining Ding & Ruyi Liu & Marek Rutkowski, 2024. "Cross-Currency Basis Swaps Referencing Backward-Looking Rates," Papers 2410.08477, arXiv.org.
    10. 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.
    11. Giacomo Bormetti & Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2018. "Impact of multiple curve dynamics in credit valuation adjustments under collateralization," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 31-44, January.
    12. 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.
    13. Damiano Brigo & Cyril Durand, 2014. "An initial approach to Risk Management of Funding Costs," Papers 1410.2034, arXiv.org.
    14. T. van der Zwaard & L. A. Grzelak & C. W. Oosterlee, 2022. "Relevance of Wrong-Way Risk in Funding Valuation Adjustments," Papers 2204.02680, arXiv.org, revised Jun 2022.
    15. Damiano Brigo & Federico Graceffa & Alexander Kalinin, 2021. "Mild to classical solutions for XVA equations under stochastic volatility," Papers 2112.11808, arXiv.org.
    16. Kun Tian & Dewen Xiong & Wenchao Yan & George Xianzhi Yuan, 2018. "The study of dynamics for credit default risk by backward stochastic differential equation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-32, December.
    17. 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.
    18. Masahiko Egami & Rusudan Kevkhishvili, 2020. "Time reversal and last passage time of diffusions with applications to credit risk management," Finance and Stochastics, Springer, vol. 24(3), pages 795-825, July.
    19. A. Itkin & V. Shcherbakov & A. Veygman, 2019. "New Model For Pricing Quanto Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-37, May.
    20. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2019. "Multi-Currency Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-35, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1602.05998. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.