IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v22y2019i03ns0219024919500158.html
   My bibliography  Save this article

A Forward Equation For Computing Derivatives Exposure

Author

Listed:
  • BERNARD LAPEYRE

    (CERMICS, École des Ponts et Chaussées. 6-8 avenue Blaise Pascal, Champs-sur-Marne, 77455 Marne la Vallée Cedex 2, France)

  • MAROUAN IBEN TAARIT

    (#x2020;Natixis, 47 quai Austerlitz, 75013, Paris, France)

Abstract

We derive a forward equation for computing the expected exposure of financial derivatives. Under general assumptions about the underlying diffusion process, we give an explicit decomposition of the exposure into an intrinsic value which can be directly deduced from the term structure of the forward mark-to-market, and a time value which expresses the variability of the future mark-to-market. Our approach is inspired by Dupire’s equation for local volatility and leads to an ordinary differential equation qualifying the evolution of the expected exposure with respect to the observation dates. We show how this approach can be linked with local times theory in dimension one and to the co-area formula in a higher dimension. As for numerical considerations, we show how this approach leads to an efficient numerical method in the case of one or two risk factors. The accuracy and time-efficiency of this forward representation in small dimension are of special interest in benchmarking XVA valuation adjustments at trade level.

Suggested Citation

  • Bernard Lapeyre & Marouan Iben Taarit, 2019. "A Forward Equation For Computing Derivatives Exposure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-26, May.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:03:n:s0219024919500158
    DOI: 10.1142/S0219024919500158
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024919500158
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024919500158?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stéphane Crépey & Rémi Gerboud & Zorana Grbac & Nathalie Ngor, 2013. "Counterparty Risk And Funding: The Four Wings Of The Tva," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-31.
    2. Coquet, F. & Ouknine, Y., 2000. "Some identities on semimartingales local times," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 149-153, August.
    Full references (including those not matched with items on IDEAS)

    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. Stéphane Crépey & Shiqi Song, 2018. "Counterparty risk and funding: immersion and beyond," Working Papers hal-01764403, HAL.
    2. Christian Bender & Christian Gärtner & Nikolaus Schweizer, 2018. "Pathwise Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 965-965, August.
    3. Yannick Armenti & Stéphane Crépey, 2017. "Central Clearing Valuation Adjustment," Working Papers hal-01169169, HAL.
    4. Stephane Crepey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2015. "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments," Papers 1502.07397, arXiv.org.
    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. Yannick Armenti & St'ephane Cr'epey, 2015. "Central Clearing Valuation Adjustment," Papers 1506.08595, arXiv.org, revised Feb 2017.
    7. Laura Morino & Wolfgang J. Ruggaldier, 2014. "On multicurve models for the term structure," Papers 1401.5431, arXiv.org.
    8. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.
    9. Stéphane Crépey & Shiqi Song, 2014. "Counterparty risk and funding: Immersion and beyond," Working Papers hal-00989062, HAL.
    10. Stéphane Crépey & Tuyet Mai Nguyen, 2018. "Nonlinear Monte Carlo schemes for counterparty risk on credit derivatives," Working Papers hal-01764400, HAL.

    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:wsi:ijtafx:v:22:y:2019:i:03:n:s0219024919500158. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.