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Variational Autoencoders for Completing the Volatility Surfaces

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  • Bienvenue Feugang Nteumagné

    (Department of Finance and Investment Management, University of Johannesburg, Johannesburg 2038, South Africa
    The initial idea for this study was conceived by C.W.S, who also assisted in the early development of the concept alongside H.A.D. B.F.N. further developed the idea, conducted the research, and drafted the manuscript. All authors contributed to reviewing and refining the final version of the paper.)

  • Hermann Azemtsa Donfack

    (Department of Finance and Investment Management, University of Johannesburg, Johannesburg 2038, South Africa
    The initial idea for this study was conceived by C.W.S, who also assisted in the early development of the concept alongside H.A.D. B.F.N. further developed the idea, conducted the research, and drafted the manuscript. All authors contributed to reviewing and refining the final version of the paper.)

  • Celestin Wafo Soh

    (Department of Finance and Investment Management, University of Johannesburg, Johannesburg 2038, South Africa
    Department of Mathematics and Stantistical Sciences, College of Science Engineering and Technology, Jackson State University, Jackson, MS 39217, USA
    The initial idea for this study was conceived by C.W.S, who also assisted in the early development of the concept alongside H.A.D. B.F.N. further developed the idea, conducted the research, and drafted the manuscript. All authors contributed to reviewing and refining the final version of the paper.)

Abstract

Variational autoencoders (VAEs) have emerged as a promising tool for modeling volatility surfaces, with particular significance for generating synthetic implied volatility scenarios that enhance risk management capabilities. This study evaluates VAE performance using synthetic volatility surfaces, chosen specifically for their arbitrage-free properties and clean data characteristics. Through a comprehensive comparison with traditional methods including thin-plate spline interpolation, parametric models (SABR and SVI), and deterministic autoencoders, we demonstrate that our VAE approach with latent space optimization consistently outperforms existing methods, particularly in scenarios with extreme data sparsity. Our findings show that accurate, arbitrage-free surface reconstruction is achievable using only 5% of the original data points, with errors 7–12 times lower than competing approaches in high-sparsity scenarios. We rigorously validate the preservation of critical no-arbitrage conditions through probability distribution analysis and total variance strip non-intersection tests. The framework we develop overcomes traditional barriers of limited market data by generating over 13,500 synthetic surfaces for training, compared to typical market availability of fewer than 100. These capabilities have important implications for market risk analysis, derivatives pricing, and the development of more robust risk management frameworks, particularly in emerging markets or for newly introduced derivatives where historical data are scarce. Our integration of machine learning with financial theory constraints represents a significant advancement in volatility surface modeling that balances statistical accuracy with financial relevance.

Suggested Citation

  • Bienvenue Feugang Nteumagné & Hermann Azemtsa Donfack & Celestin Wafo Soh, 2025. "Variational Autoencoders for Completing the Volatility Surfaces," JRFM, MDPI, vol. 18(5), pages 1-22, April.
  • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:5:p:239-:d:1646358
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    References listed on IDEAS

    as
    1. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2021. "Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 11-27, January.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
    4. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
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