Deep Learning Approaches for Pricing Options in Stochastic Volatility Models

Research Article
Open access

Deep Learning Approaches for Pricing Options in Stochastic Volatility Models

Yang Zheng 1*
  • 1 North Carolina State University    
  • *corresponding author koroly1119@gmail.com
Published on 16 September 2025 | https://doi.org/10.54254/2754-1169/2024.26931
AEMPS Vol.217
ISSN (Print): 2754-1169
ISSN (Online): 2754-1177
ISBN (Print): 978-1-80590-363-5
ISBN (Online): 978-1-80590-364-2

Abstract

Efficient computation of option prices is essential for making quick trading decisions. This paper investigates the use of deep learning to expedite the accurate calculation of European option prices within a local volatility framework that utilizes five parameters. We compared the predictions of the deep neural networks against results obtained from the Monte Carlo method across various scenarios. Our numerical experiments indicate that the approximation network achieves satisfactory accuracy. The network performs exceptionally well within the core region of the parameter domain.

Keywords:

Local volatility model, European call option, Finite difference method, Monte Carlo simulation, Deep learning

Zheng,Y. (2025). Deep Learning Approaches for Pricing Options in Stochastic Volatility Models. Advances in Economics, Management and Political Sciences,217,69-69.
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References

[1]. Bayer C, Friz P, Gatheral J. Pricing under rough volatility [J]. Quantitative Finance, 2016, 16(6): 887-904.

[2]. Wilmott P, Howison S, Dewynne J. The mathematics of financial derivatives: a student introduction [M]. Cambridge university press, 1995.

[3]. Lipton A. Mathematical methods for foreign exchange: A financial engineer's approach [M]. World Scientific, 2001.

[4]. LeCun Y, Bengio Y, Hinton G. Deep learning [J]. nature, 2015, 521(7553): 436-444.

[5]. Cox, J. Notes on Option Pricing I: Constant Elasticity of Diffusions. Unpublished draft, Stanford University, 1975.

[6]. S.L.Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. The review of financial studies, 6(2): 327{343, 1993}.

[7]. Jichao Zhao, Matt Davison, Robert M. Corless Compact finite difference method for American option pricing, Journal of Computational and Applied Mathematics, 206, 2007, 306-321.

[8]. Bayer C, Horvath B, Muguruza A, et al. On deep pricing and calibration of (rough) stochastic volatility models [J]. Preprint.

[9]. Horvath B, Muguruza A, Tomas M. Deep learning volatility [J]. arXiv preprint arXiv: 1901.09647, 2019.

[10]. Hornik K, Stinchcombe M, White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks [J]. Neural networks, 1990, 3(5): 551-560.

[11]. Emanuel D C, MacBeth J D. Further results on the constant elasticity of variance call option pricing model [J]. Journal of Financial and Quantitative Analysis, 1982, 17(4): 533-554.

[12]. Schroder.M, Computing the constant elasticity of variance option pricing formula, Journal of  Finance, 1989: 44, Mar., 211-219.

[13]. Gatheral, J., The Volatility Surface: A Practitioners Guide, 2006, NewYork, NY: John Wiley & Sons.

Cite this article

Zheng,Y. (2025). Deep Learning Approaches for Pricing Options in Stochastic Volatility Models. Advances in Economics, Management and Political Sciences,217,69-69.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 4th International Conference on Financial Technology and Business Analysis

ISBN：978-1-80590-363-5(Print) / 978-1-80590-364-2(Online)
Editor：Lukáš Vartiak
Conference website: https://2025.icftba.org/
Conference date: 12 December 2025
Series: Advances in Economics, Management and Political Sciences
Volume number: Vol.217
ISSN：2754-1169(Print) / 2754-1177(Online)

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References

[1]. Bayer C, Friz P, Gatheral J. Pricing under rough volatility [J]. Quantitative Finance, 2016, 16(6): 887-904.

[2]. Wilmott P, Howison S, Dewynne J. The mathematics of financial derivatives: a student introduction [M]. Cambridge university press, 1995.

[3]. Lipton A. Mathematical methods for foreign exchange: A financial engineer's approach [M]. World Scientific, 2001.

[4]. LeCun Y, Bengio Y, Hinton G. Deep learning [J]. nature, 2015, 521(7553): 436-444.

[5]. Cox, J. Notes on Option Pricing I: Constant Elasticity of Diffusions. Unpublished draft, Stanford University, 1975.

[6]. S.L.Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. The review of financial studies, 6(2): 327{343, 1993}.

[7]. Jichao Zhao, Matt Davison, Robert M. Corless Compact finite difference method for American option pricing, Journal of Computational and Applied Mathematics, 206, 2007, 306-321.

[8]. Bayer C, Horvath B, Muguruza A, et al. On deep pricing and calibration of (rough) stochastic volatility models [J]. Preprint.

[9]. Horvath B, Muguruza A, Tomas M. Deep learning volatility [J]. arXiv preprint arXiv: 1901.09647, 2019.

[10]. Hornik K, Stinchcombe M, White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks [J]. Neural networks, 1990, 3(5): 551-560.

[11]. Emanuel D C, MacBeth J D. Further results on the constant elasticity of variance call option pricing model [J]. Journal of Financial and Quantitative Analysis, 1982, 17(4): 533-554.

[12]. Schroder.M, Computing the constant elasticity of variance option pricing formula, Journal of  Finance, 1989: 44, Mar., 211-219.

[13]. Gatheral, J., The Volatility Surface: A Practitioners Guide, 2006, NewYork, NY: John Wiley & Sons.

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