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calibration-of-neural-sdes-using-bayesian-methods

This repo presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs).

https://github.com/evaflonner/calibration-of-neural-sdes-using-bayesian-methods

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Repository

This repo presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs).

Basic Info
  • Host: GitHub
  • Owner: evaflonner
  • License: gpl-3.0
  • Language: Jupyter Notebook
  • Default Branch: main
  • Homepage:
  • Size: 4.1 MB
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  • Stars: 1
  • Watchers: 1
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Created over 1 year ago · Last pushed 9 months ago
Metadata Files
Readme License Citation

README.md

Consider a Neural SDE model parameterised by neural networks $\theta$ consisting of equations grafik

In this work we propose a Bayesian method to calibrate this model. The key-advantage of this approach is, that robust bounds on the implied volatility are obtained in a natural way by utilising the posterior distribution on neural network weights. This repository, which builds upon work done by Patryk Gierjatowicz, Marc Sabate-Vidales and co-authors, licensed under the GNU General Public License v3.0., consists of:

1) A general .zip file named 'BayesianNSDEcalibration_general', providing code to calibrate the neural SDE with respect to option data, including an optional flag to jointy match time series data and a floating lookback option, where the data may be generated from your favourite model or may also be real.

2) An exemplyfing .ipynb named 'BayesianNSDEcalibrationempirical', considering empirical S&P 500 implied volatility data with 10 strikes and 4 maturities to determine the prices of the corresponding European call options. The spot price of the underlying at time 0 is $S0 = 590$, $\delta=4.5$, $\sigma_{prior}=4$, the interest rate is $r = 0.060$ and dividend rate $d = 0.026$. The prices are

grafik

The reason why we take this data set as an example is that even tough the data are from 1990s, they allow for a direct comparison with the results given in the Gupta and Reisinger paper, as we choose exactly the same data and hyperparameters. The plots grafik

reveal that in contrast to the bounds on the implied volatility surface presented in Gupta and Reisinger, we obtain much tighter bounds given by the minimum and maximum implied volatility for each strike and maturity that are obtained after algorithmic convergence.

References

[1] Gierjatowicz, Patryk, Marc Sabate-Vidales, David Šiška, Lukasz Szpruch, and Žan Žurič. (2020). Robust pricing and hedging via neural SDEs.

[2] Gupta, A., and C. Reisinger. (2014). Robust calibration of financial models using Bayesian estimators. Journal of Computational Finance 17:3–36.

Owner

  • Login: evaflonner
  • Kind: user

Citation (citation.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Flonner"
  given-names: "Eva"
title: "Robust financial calibration: a Bayesian approach for neural SDEs"
version: 1
date-released: 2024-06-03
url: "https://github.com/evaflonner/Calibration-of-Neural-SDEs-using-Bayesian-Methods"

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