A Convolution-Based Heterogeneous Autoregressive Model for Implied Volatility Surface Forecasting

This paper proposes a novel framework for forecasting the implied volatility surface of Volatility Index (VIX) options by extending the traditional heterogeneous autoregressive (HAR) model into a convolution-based surface forecasting approach (ConvHAR). Unlike conventional HAR models that generate forecasts at isolated points, the extended approach captures spatial-temporal dependencies across moneyness and time-to-maturity dimensions through convolutional architectures. To further enhance predictive power, we incorporate the implied volatility surface of SPX options as an auxiliary input, motivated by the theoretical and empirical linkages between SPX and VIX markets. Empirical results show that the proposed method outperforms benchmark univariate and pointwise models in forecasting accuracy, particularly when forecasting 5–15 days ahead. Moreover, incorporating cross-market volatility information from SPX leads to further gains in performance. These findings underscore the importance of modeling surface-level dynamics and market interdependencies in volatility forecasting, with practical implications for derivative pricing and risk management.