Interpolation of missing swaption volatility data using variational autoencoders

Albeit of crucial interest for financial researchers, market-implied volatility data of European swaptions often exhibit large portions of missing quotes due to illiquidity of the underlying swaption instruments. In this case, standard stochastic interpolation tools like the common SABR model cannot be calibrated to observed 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. Up to our knowledge, our studies constitute the first-ever completely nonparametric approach to modeling swaption volatility using unsupervised learning methods while simultaneously tackling the issue of missing data. Since training data for the employed variational autoencoder model is usually sparsely available, we propose a novel method to generate synthetic swaption volatility data for training and afterwards test the robustness of our approach on real market quotes. In particular, we show that SABR interpolated volatilities 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 demonstrate how the imputation can be used to successfully set up delta-neutral portfolios for hedging purposes. © 2023, The Author(s).