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.
- Code used to generated one-day-ahead surfaces are provided for transparency but require data files not available in this repo due to usage of non-publically available data.
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 4 in article)
- Random_Surfaces.ipynb: Several randomly generated surfaces for different currency pairs (Figure 6 in article)
- Delta_Histogram.ipynb: Histogram of generated one-day-ahead surfaces using the delta-day method detailed in Section 5.8 (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.
- delta_results.pickle Contains generated surface parameters and corresponding baseline shifts