A Variational Autoencoder Approach to Conditional Generation of Possible Future Volatility Surfaces

Abstract

We develop a novel method to generate future possible implied volatility surfaces given a historical sequence of surfaces and extra features such as historical returns. The proposed model architecture is based on a conditional variational autoencoder (CVAE) that encodes historical data and a long short-term memory network (LSTM) that allows for the representation of sequences of observations. The architecture can be used to generate future surfaces conditional on any set of historical data. We apply the model to S&P500 data and show that the model is able to capture the real world dynamics.

Keywords: Implied volatility surfaces, variational autoencoders, long short-term memory

JEL Classification: G17, C22, C45, C63