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Accuracy of Deep Learning in Calibrating HJM Forward Curves

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  • Fred Espen Benth
  • Nils Detering
  • Silvia Lavagnini

Abstract

We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility operators that map the square integrable noise into the Filipovi\'{c} space of forward curves. For calibration, we specify a fully parametrized version of our model and train a neural network to approximate the true option price as a function of the model parameters. This neural network can then be used to calibrate the HJM parameters based on observed option prices. We conduct a numerical case study based on artificially generated option prices in a deterministic volatility setting. In this setting we derive closed pricing formulas, allowing us to benchmark the neural network based calibration approach. We also study calibration in illiquid markets with a large bid-ask spread. The experiments reveal a high degree of accuracy in recovering the prices after calibration, even if the original meaning of the model parameters is partly lost in the approximation step.

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  • Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2020. "Accuracy of Deep Learning in Calibrating HJM Forward Curves," Papers 2006.01911, arXiv.org, revised May 2021.
    • Handle: RePEc:arx:papers:2006.01911
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    1. Stefan Tappe, 2012. "Some Refinements of Existence Results for SPDEs Driven by Wiener Processes and Poisson Random Measures," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-24, December.
    2. Christian Bayer & Blanka Horvath & Aitor Muguruza & Benjamin Stemper & Mehdi Tomas, 2019. "On deep calibration of (rough) stochastic volatility models," Papers 1908.08806, arXiv.org.
    3. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    4. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    5. Frestad, Dennis, 2008. "Common and unique factors influencing daily swap returns in the Nordic electricity market, 1997-2005," Energy Economics, Elsevier, vol. 30(3), pages 1081-1097, May.
    6. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    7. Christian Bayer & Benjamin Stemper, 2018. "Deep calibration of rough stochastic volatility models," Papers 1810.03399, arXiv.org.
    8. Ryan Ferguson & Andrew Green, 2018. "Deeply Learning Derivatives," Papers 1809.02233, arXiv.org, revised Oct 2018.
    9. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    10. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    11. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    12. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    13. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    14. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2019. "Deep Learning Volatility," Papers 1901.09647, arXiv.org, revised Aug 2019.
    15. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
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    Cited by:

    1. Fred Espen Benth & Nils Detering & Luca Galimberti, 2022. "Pricing options on flow forwards by neural networks in Hilbert space," Papers 2202.11606, arXiv.org.
    2. Blanka Horvath & Josef Teichmann & Zan Zuric, 2021. "Deep Hedging under Rough Volatility," Papers 2102.01962, arXiv.org.

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