Multi-Step Forecast of the Implied Volatility Surface Using Deep Learning

Implied volatility is an essential input to price an option. Machine learning architectures have shown strengths in learning option pricing formulas and estimating implied volatility cross-sectionally. However, implied volatility time series forecasting is typically done using the univariate time series and often for short intervals. When a univariate implied volatility series is forecasted, important implied volatility properties such as volatility skew and the term structure are lost. More importantly, short term forecasts can’t take advantage of the long term persistence in the volatility series. The thesis attempts to bridge the gap between machine learning-based implied volatility modeling and multivariate multi-step implied volatility forecasting. The thesis contributes to the literature by modeling the entire implied volatility surface (IVS) using recurrent neural network architectures. I implement 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. I 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. I find that the ConvLSTM significantly outperforms traditional time series models, as well as the benchmark Long Short Term Memory(LSTM) model in predicting the implied volatility surface for a 1-day, 30-day, and 90-day horizon, for out-of-the-money and at-the-money calls and puts