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On Calibration of Mathematical Finance Models by Hypernetworks

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Machine Learning and Knowledge Discovery in Databases: Applied Data Science and Demo Track (ECML PKDD 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14174))

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Abstract

The process of fitting mathematical finance (MF) models for option pricing - known as calibration - is expensive because evaluating the pricing function usually requires Monte-Carlo sampling. Inspired by the success of deep learning for simulation, we present a hypernetwork based approach to improve the efficiency of calibration by several orders of magnitude. We first introduce a proxy neural network to mimic the behaviour of a given mathematical finance model. The parameters of this proxy network are produced by a hyper-network conditioned on the parameters of the corresponding MF model. Training the hyper network with pseudo-data fits a family of proxy networks that can mimic any MF model given its parameters, and produce accurate prices. This amortises the cost of MF model fitting, which can now be performed rapidly for any asset by optimising w.r.t. the input of the hypernetwork. Our method is evaluated with S &P 500 index option data covering three million contracts over 15 years, and the empirical results show it performs very closely to the gold standard of calibrating the mathematical finance models directly, while boosting the speed of calibration by 500 times. The code is released at https://github.com/qmfin/HyperCalibration.

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Author information

Authors and Affiliations

  1. Queen Mary University of London, London, UK

    Yongxin Yang

  2. University of Edinburgh, Edinburgh, Scotland

    Timothy M. Hospedales

  3. Samsung AI Centre, Cambridge, UK

    Timothy M. Hospedales

Authors
  1. Yongxin Yang
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  2. Timothy M. Hospedales
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Corresponding author

Correspondence to Yongxin Yang .

Editor information

Editors and Affiliations

  1. CENTAI, Turin, Italy

    Gianmarco De Francisci Morales

  2. NYU and Two Sigma, New York, NY, USA

    Claudia Perlich

  3. Netflix, Los Angeles, CA, USA

    Natali Ruchansky

  4. Telefonica Research, Barcelona, Spain

    Nicolas Kourtellis

  5. Politecnico di Torino, Turin, Italy

    Elena Baralis

  6. CENTAI, Turin, Italy

    Francesco Bonchi

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Yang, Y., Hospedales, T.M. (2023). On Calibration of Mathematical Finance Models by Hypernetworks. In: De Francisci Morales, G., Perlich, C., Ruchansky, N., Kourtellis, N., Baralis, E., Bonchi, F. (eds) Machine Learning and Knowledge Discovery in Databases: Applied Data Science and Demo Track. ECML PKDD 2023. Lecture Notes in Computer Science(), vol 14174. Springer, Cham. https://doi.org/10.1007/978-3-031-43427-3_14

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  • DOI: https://doi.org/10.1007/978-3-031-43427-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43426-6

  • Online ISBN: 978-3-031-43427-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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