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Robust Pricing and Hedging via Neural SDEs

Code of numerical experiments in this paper.

  @misc{gierjatowicz2020robust,
  title={Robust pricing and hedging via neural SDEs},
  author={Patryk Gierjatowicz and Marc Sabate-Vidales and David Šiška and Lukasz Szpruch and Žan Žurič},
  year={2020},
  eprint={2007.04154},
  archivePrefix={arXiv},
  primaryClass={q-fin.MF}

}

...

Target data

The file Call_prices_59.pt contains the target Vanilla call option prices generated with Heston model for bi-monthly maturities up to 1 year, and 21 different strikes between K=0.8 and K=1.2.

Heston

Heston model parameters:

params

Resulting target IV surface:

Target data

Scripts

  • nsde_LV.py: Calibration to target prices of Neural SDE using Local Volatility model.

    python nsde_LV.py --device 0 --vNetWidth 50 --n_layers 20

  • nsde_LSV.py: Calibration to target prices of Neural SDE using Local Stochastic Volatility model, where \sigma^S, b^V and \sigma^V are feed-forward neural networks: LSV

    python nsde_LV.py --device 0 --vNetWidth 50 --n_layers 20