Dynamic Correlation Multivariate Stochastic Volatility Black-Litterman With Latent Factors

In finance, it is often of interest to study market volatility for portfolios that may consist of a large number of assets using multivariate stochastic volatility models. However, such models, though useful, do not usually incorporate investor views that might be available. In this paper we introduce a novel hierarchical Bayesian methodology of modeling volatility for a large portfolio of assets that incorporates investor’s personal views of the market via the Black-Litterman (BL) model. We extend the scope and use of BL models by using it within a multivariate stochastic volatility model based on latent factors for dimensionality reduction but allows for time varying correlations. Detailed derivations of MCMC algorithm are provided with an illustration with S&P500 asset returns. Moreover, sensitivity analysis for the confidence levels that the investor has in their personal views is also explored. Numerical results show that the proposed method provides flexible interpretation based on the investor’s uncertainty in personal beliefs, and converges to the empirical sample estimate when their confidence level of the market becomes weak.

A GARCH Tutorial with R

ABSTRACT Context: modeling volatility is an advanced technique in financial econometrics, with several applications for academic research. Objective: in this tutorial paper, we will address the topic of volatility modeling in R. We will discuss the underlying logic of GARCH models, their representation and estimation process, along with a descriptive example of a real-world application of volatility modeling. Methods: we use a GARCH model to predict how much time it will take, after the latest crisis, for the Ibovespa index to reach its historical peak once again. The empirical data covers the period between years 2000 and 2020, including the 2009 financial crisis and the current 2020’s episode of the COVID-19 pandemic. Conclusion: we find that, according to our GARCH model, Ibovespa is more likely than not to reach its peak once again in one year and four months from June 2020. All data and R code used to produce this tutorial are freely available on the internet and all results can be easily replicated.

Modeling Volatility Characteristics of Epileptic EEGs using GARCH Models

Objective: To determine if there was a difference in the volatility characteristics of seizure and non-seizure onset channels in the intracranial electroencephalogram (EEG) in a patient with temporal lobe epilepsy. Methods: The half-life of volatility for the different EEG channels was determined using Autoregressive Moving Average–Generalized Autoregressive Conditional Heteroscedasticity (ARMA–GARCH) models; confidence intervals were constructed using the delta method and an asymptotic method for comparing the half-lives. Results: Clinically determined seizure onsets occurred over strip electrodes named RAST (Right Anterior Subtemporal) and RMST (Right Mid Subtemporal), at locations 2, 3 and 4, on the strip electrodes. The half-lives of volatility for two of the three seizure channels, RAST3 and RAST4, were found to be significantly lower the rest of the channels for six one-minute EEG segments prior to seizure onset and nine one-minute EEG segments of an awake state. The half-lives of volatility for RAST3 and RAST4 were not significantly different to the non-seizure channels for ten one-minute segments of sleep and ten one-minute segments of sleep-to-awake states. The estimates for the half-lives were consistent for randomly selected one-minute EEG segments. Conclusions: The use of GARCH models may be a useful tool in determining hidden properties in epileptiform EEGs that may lead to better understanding of the seizure generating process.