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Forecasting VIX using Bayesian Deep Learning

Héctor J. Hortúa, Andrés Mora-Valencia

TL;DR

This paper claims 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.

Abstract

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.

Forecasting VIX using Bayesian Deep Learning

TL;DR

This paper claims 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.

Abstract

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.
Paper Structure (21 sections, 11 equations, 32 figures, 3 tables)

This paper contains 21 sections, 11 equations, 32 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Neural Networks
  4. WaveNet
  5. Temporal Convolutional Network (TCN)
  6. Transformer
  7. Bayesian Neural Networks
  8. Reparameterization Trick
  9. Flipout
  10. Multiplicative Normalizing Flows
  11. Calibration
  12. Data
  13. Methodology
  14. Results
  15. Deterministic Models
  16. ...and 6 more sections

Figures (32)

  • Figure 1: VIX historical price. Daily VIX price taken from August 22, 2013 to July 31, 2023. A peak is observed on March 2020 due to effect of Covid pandemic statement by the World Health Organization (WHO) on financial markets.
  • Figure 2: Prediction of the deterministic WaveNet model for VIX test dataset. A good fit of the model is observed except for the peaks at the beginning of the graph.
  • Figure 3: Prediction of the deterministic TCN model for VIX test dataset. A good fit of the model is observed except for the low values of the VIX at the end of the graph.
  • Figure 4: Prediction of the deterministic Transformer model for VIX test dataset. A good fit of the model is observed except for the peaks at the beginning of the graph.
  • Figure 5: Calibration diagram for the WaveNet with RT model. After minimizing the RMSCE, the scaling factor is equal to 0.7373. The dashed diagonal line represents a perfect calibration.
  • ...and 27 more figures