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

TL;DR

This paper introduces a novel method using variational autoencoders and Gibbs sampling to accurately interpolate missing implied volatility data of European swaptions, improving calibration and hedging strategies.

Contribution

It proposes a stochastic latent space approach with variational autoencoders for imputing missing swaption volatility data, enhancing calibration accuracy in illiquid markets.

Findings

Imputed volatility estimates are within two basis points of complete data calibrations.

The approach is robust even when trained on synthetic data and applied to real market quotes.

Imputation enables effective setup of delta-neutral hedging portfolios.

Abstract

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.