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Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models

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  • Blanka Horvath
  • Aitor Muguruza
  • Mehdi Tomas

Abstract

We present a neural network-based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models—including second-generation stochastic volatility models and the rough volatility family—and a range of derivative contracts. Neural networks in this work are used in an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. The form in which information from available data is extracted and used influences network performance: The grid-based algorithm used for calibration is inspired by representing the implied volatility and option prices as a collection of pixels. We highlight how this perspective opens new horizons for quantitative modelling. The calibration bottleneck posed by a slow pricing of derivative contracts is lifted, and stochastic volatility models (classical and rough) can be handled in great generality as the framework also allows taking the forward variance curve as an input. We demonstrate the calibration performance both on simulated and historical data, on different derivative contracts and on a number of example models of increasing complexity, and also showcase some of the potentials of this approach towards model recognition. The algorithm and examples are provided in the Github repository GitHub: NN-StochVol-Calibrations.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:21:y:2021:i:1:p:11-27
    DOI: 10.1080/14697688.2020.1817974
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    Cited by:

    1. Anthony Coache & Sebastian Jaimungal, 2021. "Reinforcement Learning with Dynamic Convex Risk Measures," Papers 2112.13414, arXiv.org, revised Nov 2022.
    2. Alessandro Gnoatto & Martino Grasselli & Eckhard Platen, 2022. "Calibration to FX triangles of the 4/2 model under the benchmark approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 1-34, June.
    3. Jiří Witzany & Milan Fičura, 2023. "Machine Learning Applications to Valuation of Options on Non-liquid Markets," FFA Working Papers 5.001, Prague University of Economics and Business, revised 24 Jan 2023.
    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. Andrew Na & Meixin Zhang & Justin Wan, 2023. "Computing Volatility Surfaces using Generative Adversarial Networks with Minimal Arbitrage Violations," Papers 2304.13128, arXiv.org, revised Dec 2023.
    6. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    7. Mark Kiermayer & Christian Wei{ss}, 2022. "Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance," Papers 2201.02397, arXiv.org.
    8. Ofelia Bonesini & Giorgia Callegaro & Martino Grasselli & Gilles Pag`es, 2023. "From elephant to goldfish (and back): memory in stochastic Volterra processes," Papers 2306.02708, arXiv.org, revised Sep 2023.
    9. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Working Papers hal-03902513, HAL.
    10. Jan Matas & Jan Pospíšil, 2023. "Robustness and sensitivity analyses of rough Volterra stochastic volatility models," Annals of Finance, Springer, vol. 19(4), pages 523-543, December.
    11. Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    12. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    13. Han, Xiaohui & Dong, Jianping, 2023. "Applications of fractional gradient descent method with adaptive momentum in BP neural networks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    14. Mathieu Rosenbaum & Jianfei Zhang, 2021. "Deep calibration of the quadratic rough Heston model," Papers 2107.01611, arXiv.org, revised May 2022.
    15. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Post-Print hal-02910724, HAL.
    16. Laurens Van Mieghem & Antonis Papapantoleon & Jonas Papazoglou-Hennig, 2023. "Machine learning for option pricing: an empirical investigation of network architectures," Papers 2307.07657, arXiv.org.
    17. Valentin Tissot-Daguette, 2021. "Projection of Functionals and Fast Pricing of Exotic Options," Papers 2111.03713, arXiv.org, revised Apr 2022.
    18. Masanori Hirano & Kentaro Minami & Kentaro Imajo, 2023. "Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling," Papers 2307.13217, arXiv.org.
    19. Fabio Baschetti & Giacomo Bormetti & Pietro Rossi, 2023. "Deep calibration with random grids," Papers 2306.11061, arXiv.org, revised Jan 2024.
    20. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Papers 2212.08297, arXiv.org.
    21. Joel P. Villarino & 'Alvaro Leitao & Jos'e A. Garc'ia-Rodr'iguez, 2022. "Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk," Papers 2210.02175, arXiv.org.
    22. Abir Sridi & Paul Bilokon, 2023. "Applying Deep Learning to Calibrate Stochastic Volatility Models," Papers 2309.07843, arXiv.org, revised Sep 2023.
    23. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Learning for Exotic Option Valuation," Papers 2103.12551, arXiv.org, revised Sep 2021.
    24. Bihao Su & Chenglong Xu & Jingchao Li, 2022. "A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(9), pages 1-21, May.

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