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Machine learning with kernels for portfolio valuation and risk management

Author

Listed:
  • Lotfi Boudabsa

    (EPFL)

  • Damir Filipović

    (EPFL
    Swiss Finance Institute)

Abstract

We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel. We show asymptotic consistency and derive finite-sample error bounds under conditions that are suitable for finance applications. Numerical experiments show good results in large dimensions for a moderate training sample size.

Suggested Citation

  • Lotfi Boudabsa & Damir Filipović, 2022. "Machine learning with kernels for portfolio valuation and risk management," Finance and Stochastics, Springer, vol. 26(2), pages 131-172, April.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-021-00465-4
    DOI: 10.1007/s00780-021-00465-4
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    References listed on IDEAS

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    1. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    2. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
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    4. Damir Filipovi'c & Kathrin Glau & Yuji Nakatsukasa & Francesco Statti, 2019. "Weighted Monte Carlo with least squares and randomized extended Kaczmarz for option pricing," Papers 1910.07241, arXiv.org.
    5. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    6. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    7. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    8. Mathieu Cambou & Damir Filipović, 2018. "Replicating portfolio approach to capital calculation," Finance and Stochastics, Springer, vol. 22(1), pages 181-203, January.
    9. Damir Filipović & Kathrin Glau & Yuji Nakatsukasa & Francesco Statti, 2019. "Weighted Monte Carlo with Least Squares and Randomized Extended Kaczmarz for Option Pricing," Swiss Finance Institute Research Paper Series 19-54, Swiss Finance Institute.
    10. Mathieu Cambou & Damir Filipović, 2017. "Model Uncertainty And Scenario Aggregation," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 534-567, April.
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    Cited by:

    1. 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.
    2. Lotfi Boudabsa & Damir Filipovi'c, 2022. "Ensemble learning for portfolio valuation and risk management," Papers 2204.05926, arXiv.org.

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    More about this item

    Keywords

    Dynamic portfolio valuation; Kernel ridge regression; Learning theory; Reproducing kernel Hilbert space; Portfolio risk management;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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