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Automated Option Pricing: Numerical Methods

Author

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  • PIERRE HENRY-LABORDÈRE

    (Société Générale, Global Markets, Quantitative Research, 17 cours Valmy, La Défense, France)

Abstract

In this paper, we investigate model-independent bounds for option prices given a set of market instruments. This super-replication problem can be written as a semi-infinite linear programing problem. As these super-replication prices can be large and the densities ℚ which achieve the upper bounds quite singular, we restrict ℚ to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral weighted Monte Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.

Suggested Citation

  • Pierre Henry-Labordère, 2013. "Automated Option Pricing: Numerical Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-27.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500428
    DOI: 10.1142/S0219024913500428
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    References listed on IDEAS

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    1. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2013. "Maximum Maximum of Martingales given Marginals," Working Papers hal-00684005, HAL.
    2. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1999. "Calibrating Volatility Surfaces Via Relative-Entropy Minimization," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 4, pages 121-151, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Pierre Henry-Labordère, 2019. "(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-Dual Algorithm," Working Papers hal-02095222, HAL.
    2. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    3. Sester, Julian, 2024. "A multi-marginal c-convex duality theorem for martingale optimal transport," Statistics & Probability Letters, Elsevier, vol. 210(C).

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    2. Dolinsky, Yan & Soner, H. Mete, 2015. "Martingale optimal transport in the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3893-3931.

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