Code repository for demos of the article 'Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders'. A preprint of the article can be found at: https://arxiv.org/abs/2108.04941 .

This repository contains files used to generate some of the figures found in the paper, a short demo on how to fit the CTMC-SDE (CTMC) model, and how to fit the CTMC_VAE using some precomputed outputs.

IMPORTANT NOTES

• We provide a single day's sample Implied Volatilities to demonstrate the validity of our modeling approach.
• For simplicity all code has been ported into Python, however this significantly increases the run time of some notebooks, in particular CTMC_Model_Fitting.ipynb.

Description of files Notebooks: Detailed descriptions are provide inside of each.

• CTMC_Model_Fitting.ipynb: Fitting of the CTMC model on a single day's IV data
• CTMC_VAE_Fit.ipynb: Fitting of the CTMC-VAE model on precomputed CTMC model parameters.
• Pairwise_param_scatter.ipynb: Scatter plots of generated parameters of the CTMC-VAE model (Figure 5 in article)
• Random_Surfaces.ipynb: Several randomly generated surfaces for different currency pairs (Figure 7 in article)

Python files:

• ctmc.py: Functions pertaining to computation of the price and densities of the CTMC-SDE model.
• DensityEstimation.py: Functions pertaining to computation of the spline implied density of the CTMC-SDE model.
• Fit_CTMC.py: Functions pertaining to fitting the CTMC-SDE model.
• VAE_fit.py: Functions pertaining to generation and fitting of the CTMC_VAE model.
• helpers.py: General helper functions.

Data/Networks:

• all_cur_train_valid_days_new.pickle Contains the selected training and testing days.
• ###_fitted_params.pickle Parameters of the fitted CTMC-SDE model.
• kf_days.pickle Some general precomputed statistics used for warm start in some optimizations.
• Networks/ Contains several pretrained networks of the CTMC-VAE model.