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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
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    References listed on IDEAS

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    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.
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    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.

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