IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1703.02311.html
   My bibliography  Save this paper

Mini-symposium on automatic differentiation and its applications in the financial industry

Author

Listed:
  • S'ebastien Geeraert

    (LJLL)

  • Charles-Albert Lehalle

    (LJLL)

  • Barak Pearlmutter

    (LJLL)

  • Olivier Pironneau

    (LJLL)

  • Adil Reghai

Abstract

Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic differentiation can be used. In between formal derivation and standard numerical schemes, this approach is based on software solutions applying mechanically the chain rule to obtain an exact value for the desired derivative. It has a cost in memory and cpu consumption. For participants of financial markets (banks, insurances, financial intermediaries, etc), computing derivatives is needed to obtain the sensitivity of its exposure to well-defined potential market moves. It is a way to understand variations of their balance sheets in specific cases. Since the 2008 crisis, regulation demand to compute this kind of exposure to many different case, to be sure market participants are aware and ready to face a wide spectrum of configurations. This paper shows how automatic differentiation provides a partial answer to this recent explosion of computation to perform. One part of the answer is a straightforward application of Adjoint Algorithmic Differentiation (AAD), but it is not enough. Since financial sensitivities involves specific functions and mix differentiation with Monte-Carlo simulations, dedicated tools and associated theoretical results are needed. We give here short introductions to typical cases arising when one use AAD on financial markets.

Suggested Citation

  • S'ebastien Geeraert & Charles-Albert Lehalle & Barak Pearlmutter & Olivier Pironneau & Adil Reghai, 2017. "Mini-symposium on automatic differentiation and its applications in the financial industry," Papers 1703.02311, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1703.02311
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1703.02311
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Pierre Henry-Labordere, 2012. "Counterparty Risk Valuation: A Marked Branching Diffusion Approach," Working Papers hal-00677348, HAL.
    3. Pierre Henry-Labordere, 2012. "Counterparty Risk Valuation: A Marked Branching Diffusion Approach," Papers 1203.2369, arXiv.org.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    5. Gilles Pagès & Olivier Pironneau & Guillaume Sall, 2017. "Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options," Post-Print hal-01234637, HAL.
    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. Charles-Albert Lehalle & Eyal Neuman & Segev Shlomov, 2021. "Phase Transitions in Kyle's Model with Market Maker Profit Incentives," Papers 2103.04481, arXiv.org.

    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. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    2. Zeng, Yaxiong & Klabjan, Diego & Arinez, Jorge, 2015. "Distributed solar renewable generation: Option contracts with renewable energy credit uncertainty," Energy Economics, Elsevier, vol. 48(C), pages 295-305.
    3. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    4. Work, James & Hauer, Grant & Luckert, M.K. (Marty), 2018. "What ethanol prices would induce growers to switch from agriculture to poplar in Alberta? A multiple options approach," Journal of Forest Economics, Elsevier, vol. 33(C), pages 51-62.
    5. Adam W. Kolkiewicz & Fangyuan Sally Lin, 2017. "Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 433-457, July.
    6. Kathrin Glau & Ricardo Pachon & Christian Potz, 2019. "Speed-up credit exposure calculations for pricing and risk management," Papers 1912.01280, arXiv.org.
    7. Zhengqing Zhou & Guanyang Wang & Jose Blanchet & Peter W. Glynn, 2021. "Unbiased Optimal Stopping via the MUSE," Papers 2106.02263, arXiv.org, revised Dec 2022.
    8. Dong, Wenfeng & Kang, Boda, 2019. "Analysis of a multiple year gas sales agreement with make-up, carry-forward and indexation," Energy Economics, Elsevier, vol. 79(C), pages 76-96.
    9. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    10. Marta Biancardi & Giovanni Villani, 2017. "Robust Monte Carlo Method for R&D Real Options Valuation," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 481-498, March.
    11. Gabriel J Power & Charli D. Tandja M. & Josée Bastien & Philippe Grégoire, 2015. "Measuring infrastructure investment option value," Journal of Risk Finance, Emerald Group Publishing, vol. 16(1), pages 49-72, January.
    12. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    13. Joshi, Mark & Yang, Chao, 2011. "Fast delta computations in the swap-rate market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 764-775, May.
    14. Vladislav Kargin, 2005. "Lattice Option Pricing By Multidimensional Interpolation," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647, October.
    15. Jarrow, Robert & Li, Haitao & Liu, Sheen & Wu, Chunchi, 2010. "Reduced-form valuation of callable corporate bonds: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 95(2), pages 227-248, February.
    16. Gkousis, Spiros & Welkenhuysen, Kris & Harcouët-Menou, Virginie & Pogacnik, Justin & Laenen, Ben & Compernolle, Tine, 2024. "Integrated geo-techno-economic and real options analysis of the decision to invest in a medium enthalpy deep geothermal heating plant. A case study in Northern Belgium," Energy Economics, Elsevier, vol. 134(C).
    17. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.
    18. Michèle Breton & Javier de Frutos, 2010. "Option Pricing Under GARCH Processes Using PDE Methods," Operations Research, INFORMS, vol. 58(4-part-2), pages 1148-1157, August.
    19. Xiao, Tim, 2013. "The Impact of Default Dependency and Collateralization on Asset Pricing and Credit Risk Modeling," MPRA Paper 47136, University Library of Munich, Germany.
    20. Mo, Jian-Lei & Schleich, Joachim & Zhu, Lei & Fan, Ying, 2015. "Delaying the introduction of emissions trading systems—Implications for power plant investment and operation from a multi-stage decision model," Energy Economics, Elsevier, vol. 52(PB), pages 255-264.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1703.02311. 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.