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FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

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  • Vedant Choudhary
  • Sebastian Jaimungal
  • Maxime Bergeron

Abstract

We introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability integral transform penalty to reduce model misspecification. We demonstrate that learning the joint dynamics of IV surfaces and prices produces market scenarios that are consistent with historical features and lie within the sub-manifold of surfaces that are essentially free of static arbitrage. Finally, we demonstrate that delta hedging using the simulated surfaces generates profit and loss (P&L) distributions that are consistent with realised P&Ls.

Suggested Citation

  • Vedant Choudhary & Sebastian Jaimungal & Maxime Bergeron, 2023. "FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs," Papers 2303.00859, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2303.00859
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    References listed on IDEAS

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    11. Shang, Han Lin & Kearney, Fearghal, 2022. "Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1025-1049.
    12. Yu Zheng & Yongxin Yang & Bowei Chen, 2019. "Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction," Papers 1904.12834, arXiv.org, revised May 2021.
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    Cited by:

    1. Herv'e Andr`es & Alexandre Boumezoued & Benjamin Jourdain, 2023. "Implied volatility (also) is path-dependent," Papers 2312.15950, arXiv.org.
    2. Zacharia Issa & Blanka Horvath & Maud Lemercier & Cristopher Salvi, 2023. "Non-adversarial training of Neural SDEs with signature kernel scores," Papers 2305.16274, arXiv.org.
    3. Mohamed Hamdouche & Pierre Henry-Labordere & Huyên Pham, 2023. "Generative modeling for time series via Schrödinger bridge," Working Papers hal-04063041, HAL.
    4. Kentaro Hoshisashi & Carolyn E. Phelan & Paolo Barucca, 2023. "No-Arbitrage Deep Calibration for Volatility Smile and Skewness," Papers 2310.16703, arXiv.org, revised Jan 2024.
    5. Mohamed Hamdouche & Pierre Henry-Labordere & Huy^en Pham, 2023. "Generative modeling for time series via Schr{\"o}dinger bridge," Papers 2304.05093, arXiv.org.

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