Mean-Variance-Hedging

This repository is an exploration of mean-variance hedging in discrete time, in particular the Deep Hedging strategy from Hans Buehler, Lukas Gonon, Josef Teichmann, and Ben Wood.Deep Hedging. 2018 and the dynamic programming hedging approach from Černý, Aleš, Dynamic Programming and Mean-Variance Hedging in Discrete Time (October 1, 2003)

Jupyter Notebooks are available in the examples/ folder, and also accessible online in Google Colab (listed below)

To run the examples locally, ensure that all dependencies are installed by running pip install -r requirements.txt, and ensure that the mean_variance_hedge folder is used as a directory for the corresponding utilities and functions to be used.

Documentation on how to use the functions within mean_variance_hedge is available at : https://chrischia06.github.io/Mean-Variance-Hedging/mean_variance_hedge/

Writeup

Dissertation: https://www.overleaf.com/read/jsknxnzhfpcf Slides: https://www.overleaf.com/read/zhkgygymqpwr

Notebooks

Dynamic Programming Hedge

• Colab Notebook

Deep Hedging in a Multinomial Tree setting

• examples/DeepHedgingInLattice.ipynb
• Accessible online as a Colab Notebook

Deep Hedging in the Black Scholes setting

• examples/DeepHedgingBlackScholes.ipynb
• Accessible online as a Colab Notebook

Deep Hedging in a Heston setting

• examples/DeepHedgingHeston.ipynb
• Accessible online as a Colab Notebook

Deep Hedging in a Rough Bergomi setting

• examples/DeepHedgingRoughBergomi.ipynb
• Accessible online as a Colab Notebook

References

Černý, Aleš, Dynamic Programming and Mean-Variance Hedging in Discrete Time (October 1, 2003). Applied Mathematical Finance, 2004, 11(1), 1-25, Available at SSRN: https://ssrn.com/abstract=561223

Hans Buehler, Lukas Gonon, Josef Teichmann, and Ben Wood.Deep Hedging. 2018. arXiv:1802.03042 [q-fin.CP].

• And code from: https://people.math.ethz.ch/~jteichma/index.php?content=teach_mlf2019

Johannes Ruf and Weiguan Wang.Hedging with Neural Networks. 2020.arXiv:2004.08891 [q-fin.RM]

• And code from: https://github.com/guanzi0629/Hedging_Neural_Networks

Cornelis W Oosterlee and Lech A Grzelak.Mathematical Modelling and Computation in Finance. World Scientific (Europe), 2019.

• And code from: https://github.com/LechGrzelak/Computational-Finance-Course

Ryan McCrickerd and Mikko S Pakkanen. “Turbocharging Monte Carlopricing for the rough Bergomi model”. In:Quantitative Finance18.11 (2018),pp. 1877–1886.

• And code from: https://github.com/ryanmccrickerd/rough_bergomi

Blanka Horvath, Josef Teichmann, and Zan Zuric.Deep Hedging underRough Volatility. 2021. arXiv:2102.01962 [q-fin.CP]