Multivariate Volatility Models Research Articles

Univariate and Multivariate Volatility Models for Portfolio Value at Risk

Univariate and Multivariate Volatility Models for Portfolio Value at Risk

A practical multivariate approach to testing volatility spillover

We propose an asymptotic N(0,1) inferential strategy to test for volatility spillover between markets consisting of multiple sectors. First, we use nonparametric kernel method to derive test statistics that assign flexible weight to each lag order and are able to check a growing number of lags as the sample size increases. Second, we propose a practical multivariate volatility modeling approach — which enjoys estimation consistency and simplicity — to facilitate higher dimensional spillover testing. Simulations show the reasonable finite sample performance of the proposed econometric strategy in a relatively large system. An empirical application highlights the merits of the proposed approach.

Attention to oil prices and its impact on the oil, gold and stock markets and their covariance

This paper studies the impact of investor attention to oil prices on returns, volatility, and covariances of three exchange traded funds representing oil, gold, and the stock market. For this purpose, we suggest a new multivariate volatility model based on open, high, low, and closing prices that incorporates the impact of investor attention on returns, volatility, and covariances. We find that this model, which incorporates Google searches for “oil prices” as an exogeneous variable, outperforms other considered multivariate volatility models, and demonstrates that Google searches for “oil prices” can explain and forecast covariances between returns of oil, gold, and the stock market.

Modeling and forecasting dynamic conditional correlations with opening, high, low, and closing prices

Models for variances and covariances of asset returns are crucial in risk management and asset allocation. Traditionally, these models were based on daily returns. Daily opening, high, low and closing (OHLC) prices have been sometimes used in multivariate volatility models for variances, but not for correlations. We therefore suggest a new version of the Dynamic Conditional Correlation (DCC) model wherein information from daily OHLC prices is utilized in both variance and correlation equations. The model is evaluated for two datasets: five exchange traded funds and five currencies. The results show that in terms of conditional covariance matrix estimates and forecasts the proposed model significantly outperforms, not only the standard DCC model, but also models that incorporate OHLC prices only in the variance equation.

A Bayesian analysis based on multivariate stochastic volatility model: evidence from green stocks.

Green stocks are companies environmental protective and friendly. We test Green stock index in Shanghai Stock Exchange and China Securities Index as safe-havens for global investors. Suitable multivariate-SV model and Bayesian method are used to estimate the spillover effect between different assets among local and global markets. We choose multivariate volatility model because it can efficiently simulate the spillover effect by using machine learning MCMC method. The results show that the Environmental Protection Index (EPI) of Shanghai Stock Exchange (SSE) and China Securities Index (CSI) have no significant volatility spillover from Shanghai Stock index, S &P index, gold price, oil future prices of USA and China. During COVID-19 pandemic, we find Green stock index is a suitable safe-haven with low volatility spillover. Green stock indexes has a strongly one-way spillover to the crude oil future price. Environmentally friendly investor can use diversity green assets to provide a low risk investment portfolio in EPI stock market. The DCGCt-MSV model using machine learning of MCMC method is accurate and outperform others in Bayes parameter estimation.

Multivariate Volatility Modeling of Nigerian Bank Share Prices

This study aims at finding the optimal Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) model among Diag-BEKK, Scalar-BEKK and CCC that captures the dynamics of returns in Nigerian bank share prices, using the data of daily share prices of two highly capitalized banks in Nigeria listed on the platform of Nigerian Stock Exchange (NSE) which span from 2nd January, 2009 to 28th December, 2019. Multivariate Normal and Multivariate student-t log-likelihood functions were simplified using the BHHH and Marquardt algorithm and the optimal solution was obtained using the information criteria. The BHHH and Marquardt algorithm was implemented in the GARCH 7 software of Laurent. Finally, the findings of this study showed that the Diag-Bekk (1,1) with Multivariate student-t distribution was the overall best model out of the six model combinations. Multivariate volatility modeling is therefore, recommended for bank share prices in Nigeria, and even in other banks from emerging economies.

Research on Parameter Estimation and Prediction of Sports Financial Market Volatility Model

At present, the utility function of the financial system in the sports industry has not been brought into full play. Volatility reflects the uncertainty of asset price changes and plays an important role in asset pricing, portfolio, risk management, and asset allocation. Volatility has the characteristics of thick tail, leverage, market linkage, long memory, and aggregation. There are differences between different markets and countries. Therefore, according to the complex characteristics of volatility, this paper uses the feature-oriented research method to study several volatility prediction models, namely, random volatility model, realized volatility model, and multivariate volatility model. In order to promote capital formation and alleviate the financing constraints of sports finance, it provides reference value for reducing transaction costs, improving the quality and efficiency of sports industry, and realizing sustainable and rapid development.

Bootstrapping Two-Stage Quasi-Maximum Likelihood Estimators of Time Series Models

This article provides results on the validity of bootstrap inference methods for two-stage quasi-maximum likelihood estimation involving time series data, such as those used for multivariate volatility models or copula-based models. Existing approaches require the researcher to compute and combine many first- and second-order derivatives, which can be difficult to do and is susceptible to error. Bootstrap methods are simpler to apply, allowing the substitution of capital (CPU cycles) for labor (keeping track of derivatives). We show the consistency of the bootstrap distribution and consistency of bootstrap variance estimators, thereby justifying the use of bootstrap percentile intervals and bootstrap standard errors.

Unrestricted, restricted, and regularized models for forecasting multivariate volatility

Abstract We perform an extensive investigation of different specifications of the BEKK-type multivariate volatility models for a moderate number of assets, focusing on how the degree of parametrization affects forecasting performance. Because the unrestricted specification may be too generously parameterized, often one imposes restrictions on coefficient matrices constraining them to have a diagonal or even scalar structure. We frame all three model variations (full, diagonal, scalar) as special cases of a ridge-type regularized estimator, where the off-diagonal elements are shrunk towards zero and the diagonal elements are shrunk towards homogeneity. Our forecasting experiments with BEKK-type Conditional Autoregressive Wishart model for realized volatility confirm the superiority of the more parsimonious scalar and diagonal model variations. Even though sometimes a moderate degree of regularization of the diagonal and off-diagonal parameters may be beneficial for forecasting performance, it does not regularly lead to tangible performance improvements irrespective of how precise is tuning of regularization intensity. Additionally, our results highlight the crucial importance of frequent model re-estimation in improving the forecast precision, and, perhaps paradoxically, a slight advantage of shorter estimation windows compared to longer windows.

Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model

A new multivariate volatility model that belongs to the family of conditional correlation GARCH models is introduced. The GARCH equations of this model contain a multiplicative deterministic component to describe long-run movements in volatility and, in addition, the correlations are deterministically time-varying. Parameters of the model are estimated jointly using maximum likelihood. Consistency and asymptotic normality of maximum likelihood estimators is proved. Numerical aspects of the estimation algorithm are discussed. A bivariate empirical example is provided.

COVID-19 pandemic and the crude oil market risk: hedging options with non-energy financial innovations

This study examines the hedging effectiveness of financial innovations against crude oil investment risks, both before and during the COVID-19 pandemic. We focus on the non-energy exchange traded funds (ETFs) as proxies for financial innovations given the potential positive correlation between energy variants and crude oil proxies. We employ a multivariate volatility modeling framework that accounts for important statistical features of the non-energy ETFs and oil price series in the computation of optimal weights and optimal hedging ratios. Results show evidence of hedging effectiveness for the financial innovations against oil market risks, with higher hedging performance observed during the pandemic. Overall, we show that sectoral financial innovations provide resilient investment options. Therefore, we propose that including the ETFs in an investment portfolio containing oil could improve risk-adjusted returns, especially in similar financial crisis as witnessed during the pandemic. In essence, our results are useful for investors in the global oil market seeking to maximize risk-adjusted returns when making investment decisions. Moreover, by exploring the role of structural breaks in the multivariate volatility framework, our attempts at establishing robustness for the results reveal that ignoring the same may lead to wrong conclusions about the hedging effectiveness.

Realized volatility forecast with the Bayesian random compressed multivariate HAR model

We develop a Bayesian random compressed multivariate heterogeneous autoregressive (BRC-MHAR) model to forecast the realized covariance matrices of stock returns. The proposed model randomly compresses the predictors and reduces the number of parameters. We also construct several competing multivariate volatility models with the alternative shrinkage methods to compress the parameter’s dimensions. We compare the forecast performances of the proposed models with the competing models based on both statistical and economic evaluations. The results of statistical evaluation suggest that the BRC-MHAR models have the better forecast precision than the competing models for the short-term horizon. The results of economic evaluation suggest that the BRC-MHAR models are superior to the competing models in terms of the average return, the Shape ratio and the economic value.

Modified models and simulations for estimating dynamic functional connectivity in resting state functional magnetic resonance imaging.

As understanding the nature of brain networks through dynamic functional connectivity (dFC) estimation is of paramount significant, the introduction and revision of blood-oxygen-level dependent (BOLD) signal simulation methods in brain regions and dFC estimation methods have gained significant ground in recent years. Based on the observation of BOLD signals with multivariate nonnormal distribution in functional magnetic resonance imaging (fMRI) images, we first propose a copula-based method for the production of these signals, in which nonnormal data are generated with a selected time-varying covariance matrix. Therefore, we can compare the performance of models in the cases where brain signals have a multivariate nonnormal distribution. Then, two kendallized exponentially weighted moving average (KEWMA) and kendallized dynamic conditional correlation (KDCC) multivariate volatility models are introduced which are based on two well-known and commonly used exponentially weighted moving average (EMWA) and dynamic conditional correlation (DCC) models. The results show that KDCC model can estimate conditional correlation significantly far better than the former ones (ie, DCC, standardized dynamic conditional correlation, EWMA, and standardized exponentially weighted moving average) on both types of data (ie, multivariate normal and nonnormal). In the next step, the bivariate normal distribution in Iranian resting state fMRI data is confirmed by using statistical tests, and it is shown that the dynamic nature of FC is not optimally detected using prevalent methods. Two alternative Portmanteau and rank-based tests are proposed for the examination of conditional heteroscedasticity in data. Finally, dFC in these data is estimated by employing the KDCC model.

Multivariate leverage effects and realized semicovariance GARCH models

We propose new asymmetric multivariate volatility models. The models exploit estimates of variances and covariances based on the signs of high-frequency returns, measures known as realized semivariances, semicovariances, and semicorrelations, to allow for more nuanced responses to positive and negative return shocks than threshold “leverage effect” terms traditionally used in the literature. Our empirical implementations of the new models, including extensions of widely-used bivariate GARCH specifications for a number of individual stocks and the aggregate market portfolio as well as larger dimensional dynamic conditional correlation type formulations for a cross-section of individual stocks, provide clear evidence of improved model fit and reveal new and interesting asymmetric joint dynamic dependencies.

Multivariate High-Frequency-Based Factor Model

We propose a new predictive model for large-dimensional realized covariance matrices. Using high-frequency data, we construct daily realized covariance matrices for the constituents of the S\&P 500 Index and a set of observable factors. Using a standard decomposition of the joint covariance matrix we express the covariance matrix of the individual assets similar to an approximate factor model. A novel feature of the model, is the use of the hierarchical clustering algorithm to determine the structure of the idiosyncratic covariance matrices. To construct a conditional covariance model, we suggest to model the components of the covariance structure separately using autoregressive time series regressions. In an out-of-sample portfolio selection exercise, we find that the proposed model outperforms other commonly used multivariate volatility models in extant literature.

OPEC production decisions, macroeconomic news, and volatility in the Canadian currency and oil markets

We examine the simultaneous effect of OPEC production decisions and press releases, oil and gasoline inventory surprises, as well as US and Canadian macroeconomic news announcements on oil and Canadian dollar volatilities around US and European financial crises. We use a multivariate volatility model and implement an impulse response analysis to decompose the exogenous impacts into direct and indirect effects induced by volatility spillover. We find evidence of context-specific impacts and show that 67% of the total accumulated effect of OPEC decision to maintain production on oil volatility is induced by volatility spillover from the Canadian foreign exchange rate.

Markovian lifts of positive semidefinite affine Volterra-type processes

We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model.

Range-based DCC models for covariance and value-at-risk forecasting

Abstract The dynamic conditional correlation (DCC) model by Engle (2002) is one of the most popular multivariate volatility models. This model is based solely on closing prices. It has been documented in the literature that the high and low prices of a given day can be used to obtain an efficient volatility estimation. We therefore suggest a model that incorporates high and low prices into the DCC framework. We conduct an empirical evaluation of this model on three datasets: currencies, stocks, and commodity exchange traded funds. Regardless of whether we consider in-sample fit, covariance forecasts or value-at-risk forecasts, our model outperforms not only the standard DCC model, but also an alternative range-based DCC model.

Range-Based DCC Models for Covariance and Value-at-Risk Forecasting

The dynamic conditional correlation (DCC) model by Engle (2002) is one of the most popular multivariate volatility models. This model is based solely on closing prices. It has been documented in the literature that the high and low prices of a given day can be used to obtain an efficient volatility estimation. We therefore suggest a model that incorporates high and low prices into the DCC framework. We conduct an empirical evaluation of this model on three datasets: currencies, stocks, and commodity exchange traded funds. Regardless of whether we consider in-sample fit, covariance forecasts or value-at-risk forecasts, our model outperforms not only the standard DCC model, but also an alternative range-based DCC model.

Return and Volatility Spillover among Commodity Futures, Stock Market and Exchange Rate: Evidence from India

This article aims to investigate return and volatility spillover among commodity, stock and exchange rate markets. The article further looks into whether there is any change in return and volatility spillover during the crisis and post-crisis periods and whether there is any in the behaviour of spillover changes between agro and non-agro based commodities. The study uses Vector Auto Regression followed along with by Granger causality are to understand the causality of returns. We have performed multivariate volatility model to study the volatility co-movement of different assets. Unidirectional return spillover from the Multi Commodity Exchange (non-agro commodity) to stock indices and exchange rates is found. Stock indices are found to influence exchange rates to return; whereas the only dollar explains the return in stock indices. Equity markets have been found to have a return spillover on NCDEX (agro commodity) during the post-crisis period. However, each asset market is found to have volatility spillover effects on the other asset market. Commodity indices have more spillover effects on stocks.