# Interpolation of Missing Swaption Volatility Data using Gibbs Sampling on Variational Autoencoders

arXiv: https://arxiv.org/abs/2204.10400 · HTML: https://mlsanity.com/paper/2204.10400/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 8 of 8)

- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Leveraging the Exact Likelihood of Deep Latent Variable Models](https://mlsanity.com/paper/1802.04826/) (2018)
- [Deep Smoothing of the Implied Volatility Surface](https://mlsanity.com/paper/1906.05065/) (2019)
- [Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)](https://mlsanity.com/paper/1806.04994/) (2018)
- [Data Generation as Sequential Decision Making](https://mlsanity.com/paper/1506.03504/) (2015)

## Built on by (most cited first, 1 of 1)

- [Filling in Missing FX Implied Volatilities with Uncertainties: Improving VAE-Based Volatility Imputation](https://mlsanity.com/paper/2411.05998/) (2024)

## Abstract (arXiv)

Albeit of crucial interest for both financial practitioners and researchers, market-implied volatility data of European swaptions often exhibit large portions of missing quotes due to illiquidity of the various underlying swaption instruments. In this case, standard stochastic interpolation tools like the common SABR model often cannot be calibrated to observed implied volatility smiles, due to data being only available for the at-the-money quote of the respective underlying swaption. Here, we propose to infer the geometry of the full unknown implied volatility cube by learning stochastic latent representations of implied volatility cubes via variational autoencoders, enabling inference about the missing volatility data conditional on the observed data by an approximate Gibbs sampling approach. Imputed estimates of missing quotes can afterwards be used to fit a standard stochastic volatility model. Since training data for the employed variational autoencoder model is usually sparsely available, we test the robustness of the approach for a model trained on synthetic data on real market quotes and we show that SABR interpolated volatilites calibrated to reconstructed volatility cubes with artificially imputed missing values differ by not much more than two basis points compared to SABR fits calibrated to the complete cube. Moreover, we show how the imputation can be used to successfully set up delta-neutral portfolios for hedging purposes.