Research on the Applications of Neural Network Algorithms in Deep Hedging

Research Article
Open access

Research on the Applications of Neural Network Algorithms in Deep Hedging

Chenjia Jin 1
  • 1 University of Liverpool, Liverpool, UK    
  • *corresponding author
Published on 22 March 2023 | https://doi.org/10.54254/2755-2721/2/20220659
ACE Vol.2
ISSN (Print): 2755-273X
ISSN (Online): 2755-2721
ISBN (Print): 978-1-915371-19-5
ISBN (Online): 978-1-915371-20-1

Abstract

Under market completeness assumptions, hedging a portfolio of derivatives is straightforward. In view of friction, transaction costs, liquidity and other factors, a framework is presented to extend the pricing and hedging with the hedging strategy treated as a neural network. We study the deep hedging model under incomplete market constraints such as frictions, traction cost, permanent impacts on the market and illiquidity. We discuss the limitations of certain models concerning the applications in deep hedging with constraints. After which, we analyse the advantages of different models and their joint models and find that the hedging strategy is close to the Black-Scholes delta hedging strategy. An example is also given when training after designing two hedging models. The Black-Scholes delta hedging is indeed approximated by unsupervised learning.

Keywords:

the Brownian motion, machine Learning, hedging, the Black-Scholes model

Jin,C. (2023). Research on the Applications of Neural Network Algorithms in Deep Hedging. Applied and Computational Engineering,2,512-518.
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References

[1]. Y. Dolinsky, H. M. Soner, Martingale optimal transport and robust hedging in continuous time, Proceedings of Probability Theory and Related Fields, Springer, 2014, pp. 391-427. DOI: https://doi.org/10.1007/s00440-013-0531-y

[2]. M. Nutz, H.M. Soner, Superhedging and Dynamic risk Measures under Volatility Uncertainty, Proceedings of the Industrial and Applied Mathematics, vol. 50, SIAM Journal on Control and Optimization, 2012. DOI: https://doi.org/10.1137/100814925

[3]. X. Shi, D. Xu, Z. Zhang, Deep Learning Algorithms for Hedging with Frictions, arXiv preprint, vol. 2112.04553, arXiv, 2021. DOI: https://doi.org/10.48550/arxiv.2111.01931.

[4]. J. Han, A. Jentzen, W. E., Solving high-dimensional partial differential equations using deep learning, in: Proceedings of the National Academy Sciences, 2018, pp. 8505-8510. DOI: https://doi.org/10.1073/pnas.1718942115

[5]. H. Buehler, L. Gonon, J. Teichmann, B. Wood, Deep hedging, Quantitative Finance, vol. 19, No.8, 2019, pp. 1271-1291. DOI: https://doi.org/10.1080/14697688.2019.1571683

[6]. J. Cao, J. Chen, J. Hull, Z. Poulos, Deep Hedging of Derivatives Using Reinforcement Learn-ing, in: The Journal of Financial Data Science Winter, arXiv, 2021. DOI: 10.3905/jfds.2020.1.052

[7]. A. Löffler, L. Kruschwitz, The Brownian Motion A Rigorous but Gentle Introduction for Econ-omists, Springer International Publishing, 2019. DOI: https://search-ebscohost-com.liverpool.idm.oclc.org/login.aspx?direct=true&db=cat00003a&AN=lvp.b5649694&site=eds-live&scope=site

[8]. M. Kozyra, Deep learning approach to hedging, Oxford, 2018. DOI:https://www.maths.ox.ac.uk/system/files/media/michal_kozyra.pdf

[9]. N. Boursin, C. Remlinger, J. Mikael, C. A. Hargreaves, Deep Generators on Commodity mar-kets; application to Deep Hedging, Proceedings of the Quantitative Finance, arXiv, 2022. DOI: http://arxiv.org/abs/2205.13942X

[10]. M. Mastinšek, Discrete-time delta hedging and the Black-Scholes model with transaction costs, Proceedings of the Mathematical Methods of Operations Research, Springer, 2006, pp. 227-236. DOI: https://doi.org/10.1007/s00186-006-0086-0

Cite this article

Jin,C. (2023). Research on the Applications of Neural Network Algorithms in Deep Hedging. Applied and Computational Engineering,2,512-518.

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 Computing and Data Science (CONF-CDS 2022)

ISBN：978-1-915371-19-5(Print) / 978-1-915371-20-1(Online)
Editor：Alan Wang
Conference website: https://www.confcds.org/
Conference date: 16 July 2022
Series: Applied and Computational Engineering
Volume number: Vol.2
ISSN：2755-2721(Print) / 2755-273X(Online)

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References

[1]. Y. Dolinsky, H. M. Soner, Martingale optimal transport and robust hedging in continuous time, Proceedings of Probability Theory and Related Fields, Springer, 2014, pp. 391-427. DOI: https://doi.org/10.1007/s00440-013-0531-y

[2]. M. Nutz, H.M. Soner, Superhedging and Dynamic risk Measures under Volatility Uncertainty, Proceedings of the Industrial and Applied Mathematics, vol. 50, SIAM Journal on Control and Optimization, 2012. DOI: https://doi.org/10.1137/100814925

[3]. X. Shi, D. Xu, Z. Zhang, Deep Learning Algorithms for Hedging with Frictions, arXiv preprint, vol. 2112.04553, arXiv, 2021. DOI: https://doi.org/10.48550/arxiv.2111.01931.

[4]. J. Han, A. Jentzen, W. E., Solving high-dimensional partial differential equations using deep learning, in: Proceedings of the National Academy Sciences, 2018, pp. 8505-8510. DOI: https://doi.org/10.1073/pnas.1718942115

[5]. H. Buehler, L. Gonon, J. Teichmann, B. Wood, Deep hedging, Quantitative Finance, vol. 19, No.8, 2019, pp. 1271-1291. DOI: https://doi.org/10.1080/14697688.2019.1571683

[6]. J. Cao, J. Chen, J. Hull, Z. Poulos, Deep Hedging of Derivatives Using Reinforcement Learn-ing, in: The Journal of Financial Data Science Winter, arXiv, 2021. DOI: 10.3905/jfds.2020.1.052

[7]. A. Löffler, L. Kruschwitz, The Brownian Motion A Rigorous but Gentle Introduction for Econ-omists, Springer International Publishing, 2019. DOI: https://search-ebscohost-com.liverpool.idm.oclc.org/login.aspx?direct=true&db=cat00003a&AN=lvp.b5649694&site=eds-live&scope=site

[8]. M. Kozyra, Deep learning approach to hedging, Oxford, 2018. DOI:https://www.maths.ox.ac.uk/system/files/media/michal_kozyra.pdf

[9]. N. Boursin, C. Remlinger, J. Mikael, C. A. Hargreaves, Deep Generators on Commodity mar-kets; application to Deep Hedging, Proceedings of the Quantitative Finance, arXiv, 2022. DOI: http://arxiv.org/abs/2205.13942X

[10]. M. Mastinšek, Discrete-time delta hedging and the Black-Scholes model with transaction costs, Proceedings of the Mathematical Methods of Operations Research, Springer, 2006, pp. 227-236. DOI: https://doi.org/10.1007/s00186-006-0086-0

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