Forecasting VIX Using Bayesian Deep Learning

Recently, deep learning techniques are gradually replacing traditional statistical and machine learning models as the first choice for price forecasting tasks. In this paper, we leverage probabilistic deep learning for inferring the volatility index VIX. We employ the probabilistic counterpart of WaveNet, Temporal Convolutional Network (TCN), and Transformers. We show that TCN outperforms all models with an RMSE around 0.189. In addition, it has been well known that modern neural networks provide inaccurate uncertainty estimates. For solving this problem, we use the standard deviation scaling to calibrate the networks. Furthermore, we found out that MNF with Gaussian prior outperforms Reparameterization Trick and Flipout models in terms of precision and uncertainty predictions. Finally, we claim that MNF with Cauchy and LogUniform prior distributions yield well-calibrated TCN, and Transformer and WaveNet networks being the former that best infer the VIX values for one and five-step-ahead forecasting, and the probabilistic Transformer model yields an adequate forecasting for the COVID-19 pandemic period.