Session 9 - Forecasting: Multi-Step Forecast of the Implied Volatility Surface Using Deep Learning

Modeling implied volatility surface (IVS) is of paramount importance to price and hedge an option. The literature is abundant in predicting realized volatility and the VIX using time series models, but lack in predicting the whole IVS. Machine learning architectures have shown strengths in learning option pricing formulas and estimating implied volatility cross-sectionally. We attempt to bridge the gap between machine learning-based implied volatility modeling and multivariate multi-step implied volatility forecasting. We contribute to the literature by modeling the entire IVS using recurrent neural network architectures, namely Convolutional Long Short Term Memory Neural Network (ConvLSTM) to produce multivariate and multi-step forecasts of the S&P 500 implied volatility surface. The ConvLSTM model is capable of understanding the spatiotemporal relationships between strikes and maturities (term structure), and of modeling volatility surface dynamics non-parametrically.Using the daily S&P 500 index options from 2002 to 2019, we benchmark the ConvLSTM model against traditional multivariate time series Vector autoregression (VAR), Vector Error Correction (VEC) model, and deep learning-based Long-Short-Term Memory (LSTM) neural network. We find that both LSTM and ConvLSTM can fit the training (sample) data extremely well with mean absolute percentage error (MAPE) being 3.56% and 3.88%, respectively. As for out-of-sample data, the ConvLSTM (8.26% ) model significantly outperforms traditional time series models (13.72% MAPE), as well as the benchmark Long Short Term Memory (LSTM) model (18.74%) in predicting the implied volatility surface for a 1-day, 30-day, and 90-day horizon, for all moneyness groups and contract months of both calls and puts.