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A machine learning approach to portfolio pricing and risk management for high-dimensional problems

Author

Listed:
  • Lucio Fernandez-Arjona

    (University of Zurich)

  • Damir Filipovi'c

    (EPFL and Swiss Finance Institute)

Abstract

We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an effective low-dimensional representation, overcoming the curse of dimensionality common to function approximation in high-dimensional spaces. We show results based on polynomial and neural network bases. Both offer superior results to naive Monte Carlo methods and other existing methods like least-squares Monte Carlo and replicating portfolios.

Suggested Citation

  • Lucio Fernandez-Arjona & Damir Filipovi'c, 2020. "A machine learning approach to portfolio pricing and risk management for high-dimensional problems," Papers 2004.14149, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2004.14149
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    File URL: http://arxiv.org/pdf/2004.14149
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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.
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    3. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245, July.
    4. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    5. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    6. 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.
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    Cited by:

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    2. Yuji Shinozaki, 2024. "A Review of New Developments in Finance with Deep Learning: Deep Hedging and Deep Calibration," IMES Discussion Paper Series 24-E-02, Institute for Monetary and Economic Studies, Bank of Japan.
    3. Laurens Van Mieghem & Antonis Papapantoleon & Jonas Papazoglou-Hennig, 2023. "Machine learning for option pricing: an empirical investigation of network architectures," Papers 2307.07657, arXiv.org.

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