  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 WaveNet networks
being the former that best infer the VIX values.
