Pricing options and computing implied volatilities using neural networks

Shuaiqiang Liu; Cornelis W. Oosterlee; Sander M. Bohte

doi:10.3390/risks7010016

Pricing options and computing implied volatilities using neural networks

Shuaiqiang Liu^*
, Cornelis W. Oosterlee
, Sander M. Bohte

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

Original language	English
Article number	16
Journal	Risks
Volume	7
Issue number	1
DOIs	https://doi.org/10.3390/risks7010016
Publication status	Published - Mar 2019
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgments: The authors would like to thank the China Scholarship Council (CSC) for the financial support. This research was conducted using the supercomputer Little Green Machine II in the Netherlands.

Publisher Copyright:
© 2019 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

Acknowledgments: The authors would like to thank the China Scholarship Council (CSC) for the financial support. This research was conducted using the supercomputer Little Green Machine II in the Netherlands.

Keywords

Black-Scholes
Computational finance
GPU
Heston
Implied volatility
Machine learning
Neural networks
Option pricing

Access to Document

10.3390/risks7010016

Cite this

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title = "Pricing options and computing implied volatilities using neural networks",

abstract = "This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent{\textquoteright}s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.",

keywords = "Black-Scholes, Computational finance, GPU, Heston, Implied volatility, Machine learning, Neural networks, Option pricing",

author = "Shuaiqiang Liu and Oosterlee, \{Cornelis W.\} and Bohte, \{Sander M.\}",

note = "Funding Information: Acknowledgments: The authors would like to thank the China Scholarship Council (CSC) for the financial support. This research was conducted using the supercomputer Little Green Machine II in the Netherlands. Publisher Copyright: {\textcopyright} 2019 by the authors. Licensee MDPI, Basel, Switzerland.",

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doi = "10.3390/risks7010016",

language = "English",

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AU - Oosterlee, Cornelis W.

AU - Bohte, Sander M.

N1 - Funding Information: Acknowledgments: The authors would like to thank the China Scholarship Council (CSC) for the financial support. This research was conducted using the supercomputer Little Green Machine II in the Netherlands. Publisher Copyright: © 2019 by the authors. Licensee MDPI, Basel, Switzerland.

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N2 - This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

AB - This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

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KW - Heston

KW - Implied volatility

KW - Machine learning

KW - Neural networks

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Pricing options and computing implied volatilities using neural networks

Abstract

Bibliographical note

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Keywords

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