Interpolation of Missing Swaption Volatility Data using Gibbs Sampling on Variational Autoencoders
This addresses a data interpolation issue for financial practitioners and researchers in derivatives markets, offering an incremental improvement over existing methods.
The paper tackles the problem of missing swaption volatility data due to illiquidity by using variational autoencoders with Gibbs sampling to infer and impute missing values, showing that SABR model fits based on reconstructed data differ by not much more than two basis points from those using complete data.
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.