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A Bayesian take on option pricing with Gaussian processes

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  • Martin Tegner
  • Stephen Roberts

Abstract

Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it to data. In this paper we present novel Bayesian inference with Gaussian process priors. We obtain a rich representation of the local volatility function with a probabilistic notion of uncertainty attached to the calibrate. We propose an inference algorithm and apply our approach to S&P 500 market data.

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  • Martin Tegner & Stephen Roberts, 2021. "A Bayesian take on option pricing with Gaussian processes," Papers 2112.03718, arXiv.org.
    • Handle: RePEc:arx:papers:2112.03718
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    File URL: http://arxiv.org/pdf/2112.03718
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    References listed on IDEAS

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    1. Jacquier, Eric & Jarrow, Robert, 2000. "Bayesian analysis of contingent claim model error," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 145-180.
    2. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
    3. Ben Hambly & Matthieu Mariapragassam & Christoph Reisinger, 2016. "A forward equation for barrier options under the Brunick & Shreve Markovian projection," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 827-838, June.
    4. Ben Hambly & Matthieu Mariapragassam & Christoph Reisinger, 2014. "A Forward Equation for Barrier Options under the Brunick&Shreve Markovian Projection," Papers 1411.3618, arXiv.org, revised Sep 2016.
    5. Carl Chiarella & Mark Craddock & Nadima El-Hassan, 2000. "The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology," Research Paper Series 39, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Sana Ben Hamida & Rama Cont, 2005. "Recovering Volatility from Option Prices by Evolutionary Optimization," Post-Print hal-02490586, HAL.
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    Cited by:

    1. Christa Cuchiero & Eva Flonner & Kevin Kurt, 2024. "Robust financial calibration: a Bayesian approach for neural SDEs," Papers 2409.06551, arXiv.org, revised Sep 2024.

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