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Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics

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  • Andrew Lesniewski
  • Giulio Trigila

Abstract

We propose a highly efficient and accurate methodology for generating synthetic financial market data using a diffusion model approach. The synthetic data produced by our methodology align closely with observed market data in several key aspects: (i) they pass the two-sample Cramer - von Mises test for portfolios of assets, and (ii) Q - Q plots demonstrate consistency across quantiles, including in the tails, between observed and generated market data. Moreover, the covariance matrices derived from a large set of synthetic market data exhibit significantly lower condition numbers compared to the estimated covariance matrices of the observed data. This property makes them suitable for use as regularized versions of the latter. For model training, we develop an efficient and fast algorithm based on numerical integration rather than Monte Carlo simulations. The methodology is tested on a large set of equity data.

Suggested Citation

  • Andrew Lesniewski & Giulio Trigila, 2024. "Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics," Papers 2412.00036, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2412.00036
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Magnus Wiese & Robert Knobloch & Ralf Korn & Peter Kretschmer, 2020. "Quant GANs: deep generation of financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 20(9), pages 1419-1440, September.
    3. Kasper Johansson & Mehmet Giray Ogut & Markus Pelger & Thomas Schmelzer & Stephen Boyd, 2023. "A Simple Method for Predicting Covariance Matrices of Financial Returns," Papers 2305.19484, arXiv.org, revised Nov 2023.
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