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Arbitrage-free neural-SDE market models

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  • Samuel N. Cohen
  • Christoph Reisinger
  • Sheng Wang

Abstract

Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting underlying financial constraints and while being practically implementable. We derive a state space for prices which are free from static (or model-independent) arbitrage and study the inference problem where a model is learnt from discrete time series data of stock and option prices. We use neural networks as function approximators for the drift and diffusion of the modelled SDE system, and impose constraints on the neural nets such that no-arbitrage conditions are preserved. In particular, we give methods to calibrate \textit{neural SDE} models which are guaranteed to satisfy a set of linear inequalities. We validate our approach with numerical experiments using data generated from a Heston stochastic local volatility model.

Suggested Citation

  • Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2021. "Arbitrage-free neural-SDE market models," Papers 2105.11053, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:2105.11053
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    References listed on IDEAS

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    Cited by:

    1. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Hedging option books using neural-SDE market models," Papers 2205.15991, arXiv.org.
    2. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Estimating risks of option books using neural-SDE market models," Papers 2202.07148, arXiv.org.
    3. Magnus Wiese & Ben Wood & Alexandre Pachoud & Ralf Korn & Hans Buehler & Phillip Murray & Lianjun Bai, 2021. "Multi-Asset Spot and Option Market Simulation," Papers 2112.06823, arXiv.org.
    4. Bernhard Hientzsch, 2023. "Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging," Papers 2401.08600, arXiv.org.
    5. Brian Ning & Sebastian Jaimungal & Xiaorong Zhang & Maxime Bergeron, 2021. "Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders," Papers 2108.04941, arXiv.org, revised Jan 2022.
    6. Christa Cuchiero & Philipp Schmocker & Josef Teichmann, 2023. "Global universal approximation of functional input maps on weighted spaces," Papers 2306.03303, arXiv.org, revised Feb 2024.
    7. Beatrice Acciaio & Anastasis Kratsios & Gudmund Pammer, 2022. "Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer," Papers 2201.13094, arXiv.org, revised Mar 2023.
    8. Christa Cuchiero & Guido Gazzani & Sara Svaluto-Ferro, 2022. "Signature-based models: theory and calibration," Papers 2207.13136, arXiv.org.
    9. Yannick Limmer & Blanka Horvath, 2023. "Robust Hedging GANs," Papers 2307.02310, arXiv.org.
    10. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org.

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