DeepVol: Volatility Forecasting from High-Frequency Data with Dilated Causal Convolutions

TL;DR

DeepVol tackles day-ahead realised volatility forecasting by leveraging raw high-frequency intraday data with a Dilated Causal Convolution network. It avoids preprocessing into realised measures, instead learning from intraday signals with a large receptive field and an attention mechanism to weight inputs. On two years of NASDAQ-100 data, DeepVol outperforms traditional ARCH/GARCH-based baselines and realised-measures models, including during volatility shocks, and demonstrates transfer learning to unseen stocks. The work highlights the practical potential of data-driven, high-frequency–aware architectures for risk management and derivatives pricing, where rapid adaptation and robust performance are crucial.

Abstract

Volatility forecasts play a central role among equity risk measures. Besides traditional statistical models, modern forecasting techniques based on machine learning can be employed when treating volatility as a univariate, daily time-series. Moreover, econometric studies have shown that increasing the number of daily observations with high-frequency intraday data helps to improve volatility predictions. In this work, we propose DeepVol, a model based on Dilated Causal Convolutions that uses high-frequency data to forecast day-ahead volatility. Our empirical findings demonstrate that dilated convolutional filters are highly effective at extracting relevant information from intraday financial time-series, proving that this architecture can effectively leverage predictive information present in high-frequency data that would otherwise be lost if realised measures were precomputed. Simultaneously, dilated convolutional filters trained with intraday high-frequency data help us avoid the limitations of models that use daily data, such as model misspecification or manually designed handcrafted features, whose devise involves optimising the trade-off between accuracy and computational efficiency and makes models prone to lack of adaptation into changing circumstances. In our analysis, we use two years of intraday data from NASDAQ-100 to evaluate the performance of DeepVol. Our empirical results suggest that the proposed deep learning-based approach effectively learns global features from high-frequency data, resulting in more accurate predictions compared to traditional methodologies and producing more accurate risk measures.

Figures (9)

• Figure 1: Apple's daily data. The top row shows the price trend, while the second row depicts the associated daily returns. In the bottom row, an estimation of the unobserved latent volatility process is calculated using a 5-day moving window over the daily returns. Notice that this method of estimating the volatility serves just as an approximation to the underlying latent volatility process, providing insights into the dynamic nature of market volatility.
• Figure 2: Left: Distribution of daily returns. Right: Distribution of realised volatility (in logs).
• Figure 3: The blue curve represents the cross-sectional average of daily returns across the analysed stocks, with the green area covering the 25-th percentile to the 75-th percentile, and the red area covering the 5-th percentile to the 95-th percentile.
• Figure 4: The blue curve represents cross-sectional average of daily realised volatility across the analysed stocks, with the green area covering the 25-th percentile to the 75-th percentile, and the red area covering the 5-th percentile to the 95-th percentile.
• Figure 5: DeepVol's operation over the high-frequency data through dilated causal convolutions. The dilation factor grows exponentially, allowing an increase in the receptive field without increasing the model's complexity.