Multivariate Volatility Models Research Articles

Building a dynamic correlation network for fat-tailed financial asset returns.

In this paper, a novel approach to building a dynamic correlation network of highly volatile financial asset returns is presented. Our method avoids the spurious correlation problem when estimating the dynamic correlation matrix of financial asset returns by using a filtering approach. A multivariate volatility model, DCC–GARCH, is employed to filter the fat-tailed returns. The method is proven to be more reliable for detecting dynamic changes in the correlation matrix compared with the widely used method of calculating time-dependent correlation matrices over a fixed size moving window, which can have fundamental problems when applied to fat-tailed returns. We apply the method to selected Japanese stock returns to observe the dynamic network changes as a case study. The estimated time-dependent correlation matrices are then compared with those calculated by using the traditional method to highlight the advantages of the proposed method. Two types of indicators, namely the largest eigenvalue and cosine distance measures, are introduced to identify significant changes in the correlation matrix for an initial screening of remarkable stress events. A more detailed network-based analysis is then conducted by examining topological measures calculated from the network adjacency matrices. The higher density and lower heterogeneity of the correlation network during stress periods are clearly observed, while the correlation network of stock returns is shown to be robust with regard to time. The method discussed in this paper is not limited to stock returns; it can also be applied to build a dynamic correlation network of other financial and non-financial time series with high volatility.

Dynamic dependence networks: Financial time series forecasting and portfolio decisions

We discuss Bayesian forecasting of increasingly high‐dimensional time series, a key area of application of stochastic dynamic models in the financial industry and allied areas of business. Novel state‐space models characterizing sparse patterns of dependence among multiple time series extend existing multivariate volatility models to enable scaling to higher numbers of individual time series. The theory of these dynamic dependence network models shows how the individual series can be decoupled for sequential analysis and then recoupled for applied forecasting and decision analysis. Decoupling allows fast, efficient analysis of each of the series in individual univariate models that are linked – for later recoupling – through a theoretical multivariate volatility structure defined by a sparse underlying graphical model. Computational advances are especially significant in connection with model uncertainty about the sparsity patterns among series that define this graphical model; Bayesian model averaging using discounting of historical information builds substantially on this computational advance. An extensive, detailed case study showcases the use of these models and the improvements in forecasting and financial portfolio investment decisions that are achievable. Using a long series of daily international currencies, stock indices and commodity prices, the case study includes evaluations of multi‐day forecasts and Bayesian portfolio analysis with a variety of practical utility functions, as well as comparisons against commodity trading advisor benchmarks. Copyright © 2016 John Wiley & Sons, Ltd.

OTIMIZAÇÃO DE CARTEIRAS BASEADA EM MODELOS DE CORRELAÇÕES CONDICIONAIS

Modelos multivariados de volatilidade baseados em correlações condicionais têm recebido grande atenção em função da sua capacidade de modelar a dinâmica presente nas matrizes de covariâncias de retornos de ativos financeiros. Neste artigo, analisa-se o desempenho dessa classe de modelos quando aplicados ao problema de seleção de otimização de carteiras de ações. Para isso, implementam-se quatro diferentes especificações parcimoniosas de modelos de correlações condicionais da família Garch. Utilizando-se dados dos mercados acionários brasileiro e norte-americano, obtêm-se carteiras de mínima variância para cada um dos mercados. Os resultados indicam que as carteiras de variância mínima obtidas com modelos de correlações condicionais obtiveram resultados superiores em termos de menor risco, maior retorno ajustado ao risco, maior retorno bruto acumulado e maior excesso de retorno acumulado quando comparados aos principais índices de referência de cada um dos países.

Volatility and a century of energy markets dynamics

How similar is the price behavior of oil, natural gas, and coal? Are there any interactions among these three fuel prices and their volatilities? Using the Yatchew and Dimitropoulos (2016) annual data for the United States, over the period from 1870 to 2014, and state-of-the-art econometric methodology, we explore for spillovers and interactions among the three energy markets. In doing so, we use a range of univariate and multivariate volatility models. The key contribution to the literature is the estimation of a trivariate BEKK model that allows for the interdependence of oil, natural gas, and coal returns and volatilities, using the longest span prices that have ever been studied before.

Analysis of contagion from the dynamic conditional correlation model with Markov Regime switching

ABSTRACTOver the last decades, the transmissions of international financial events have been the subject of many academic studies focused on multivariate volatility models. This study evaluates the financial contagion between stock market returns. The econometric model employed, regime switching dynamic correlation (RSDC). A modification was made in the original RSDC model, the introduction of the GJR-GARCH-N and also GJR-GARCH-t models, on the equation of conditional univariate variances, thus allowing us to capture the asymmetric effects in volatility and also heavy tails. A database was built using series of indices in the United States (S&P500), the United Kingdom (FTSE100), Brazil (IBOVESPA) and South Korea (KOSPI) from 1 February 2003 to 20 September 2012. Throughout this study the methodology is compared with those frequently found in literature, and the model RSDC with two regimes was defined as the most appropriate for the selected sample with t-Student distribution in the disturbances. The adapted RSDC model used in this article can be used to detect contagion – considering the definition of financial contagion from the World Bank called very restrictive – with the help of the empirical exercise.

Estimating Multivariate Volatility Models Equation by Equation

Summary The paper investigates the estimation of a wide class of multivariate volatility models. Instead of estimating an m-multivariate volatility model, a much simpler and numerically efficient method consists in estimating m univariate generalized auto-regressive conditional heteroscedasticity type models equation by equation in the first step, and a correlation matrix in the second step. Strong consistency and asymptotic normality of the equation-by-equation estimator are established in a very general framework, including dynamic conditional correlation models. The equation-by-equation estimator can be used to test the restrictions imposed by a particular multivariate generalized auto-regressive conditional heteroscedasticity specification. For general constant conditional correlation models, we obtain the consistency and asymptotic normality of the two-step estimator. Comparisons with the global method, in which the model parameters are estimated in one step, are provided. Monte Carlo experiments and applications to financial series illustrate the interest of the approach.

Effects of Volatility of the Exchange Rate on Inflation Expectations and Growth Prospects in Mexico (2002-2014)

This paper is aimed at assessing the impact of exchange rate volatility on inflation expectations and economic growth prospects in Mexico. In order to examine whether there is some degree of causality, we will be using standard multivariate volatility models. The goal of this research is to measure the direction of causality, that is, we will analyze, econometrically, potential relationships in both directions. The main finding is that there is only a statistically significant relationship between the exchange rate volatility and the volatility of inflation expectations, while no statistically significant association with growth prospects was found; these results provide important information that could be used in monetary policy design.

Hedge Ratio Prediction with Noisy and Asynchronous High‐Frequency Data

A growing body of literature has focused on the design of covariance estimators for identifying when high‐frequency asset prices are asynchronous and contaminated by microstructure noise. This paper presents a comparison of the prediction ability of covariance estimators within a high‐frequency‐based multivariate volatility model for hedge ratio prediction. Empirical results show that the noise‐free predictions are superior to those contaminated by the noise, with the utility gains being particularly substantial for hedgers with pronounced risk aversion. The results demonstrate the importance of removing microstructure noise and asynchronous trading from covariance estimation to achieve accurate hedge ratio prediction. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:295–314, 2016

Model Uncertainty and Forecast Combination in High‐Dimensional Multivariate Volatility Prediction

AbstractIn multivariate volatility prediction, identifying the optimal forecasting model is not always a feasible task. This is mainly due to the curse of dimensionality typically affecting multivariate volatility models. In practice only a subset of the potentially available models can be effectively estimated, after imposing severe constraints on the dynamic structure of the volatility process. It follows that in most applications the working forecasting model can be severely misspecified. This situation leaves scope for the application of forecast combination strategies as a tool for improving the predictive accuracy. The aim of the paper is to propose some alternative combination strategies and compare their performances in forecasting high‐dimensional multivariate conditional covariance matrices for a portfolio of US stock returns. In particular, we will consider the combination of volatility predictions generated by multivariate GARCH models, based on daily returns, and dynamic models for realized covariance matrices, built from intra‐daily returns. Copyright © 2015 John Wiley & Sons, Ltd.

World gold prices and stock returns in China: Insights for hedging and diversification strategies

This article uses the VAR–GARCH framework of Ling and McAleer (2003) to explore both return and volatility spillovers between world gold prices and stock market in China over the period from March 22, 2004 through March 31, 2011. It further analyzes the optimal weights and hedge ratios for dedicated gold-stock portfolio holdings and show how empirical results can be used to build effective diversification and hedging strategies. Several competing multivariate volatility models which are commonly-used in the finance literature (CCC–GARCH, DCC–GARCH, diagonal BEKK–GARCH, scalar BEKK–GARCH, and full-BEKK–GARCH) are also considered for comparison purpose. Our results show evidence of significant return and volatility cross effects between gold prices and stock prices in China, as well as the superiority of the VAR-GARCH model over the other multivariate GARCH specifications. In particular, past gold returns play a crucial role in explaining the dynamics of conditional return and volatility of Chinese stock market and should thus be accounted for when forecasting future stock returns. Our portfolio analysis suggests that adding gold to a portfolio of Chinese stocks improves its risk-adjusted return and helps to effectively hedge against stock risk exposure over time. Finally, when considering the period of the recent global financial crisis, we find that the gold asset serves as a safe haven for stocks in the Chinese stock markets.

Proximity-Structured Multivariate Volatility Models

In many multivariate volatility models, the number of parameters increases faster than the cross-section dimension, hence creating a curse of dimensionality problem. This paper discusses specification and identification of structured parameterizations based on weight matrices induced by economic proximity. It is shown that structured specifications can mitigate or even solve the curse of dimensionality problem. Identification and estimation of structured specifications are analyzed, rank and order conditions for identification are given and the specification of weight matrices is discussed. Several structured specifications compare well with alternatives in modelling conditional covariances of six returns from the New York Stock Exchange.

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

We develop a new model for the multivariate covariance matrix dynamics based on daily return observations and daily realized covariance matrix kernels based on intraday data. We account for possible fat-failedness of both type of data by assuming a matrix-F distribution for the realized kernels, and a multivariate Student’s t distribution for the returns. Using score dynamics for the unobserved true covariance matrix, our approach automatically corrects for the effect of outliers and incidentally large observations, both in returns and in realized (co)variances. By an appropriate choice of scaling of the conditional score function we retain a convenient matrix formulation for the dynamic updates of the covariance matrix. This makes the model highly computationally efficient. The model performs well for both simulated and empirical data. In our empirical application, we study daily returns and realized kernels from 30 equities over the period 2001-2014 and find that the new model statistically outperforms (recently developed) multivariate volatility models, both in-sample and out-of-sample. We also comment on the possibility of composite likelihood methods for estimation.

Factor High-Frequency Based Volatility (HEAVY) Models

We propose a new class of multivariate volatility models utilizing realized measures of asset volatility and covolatility extracted from high-frequency data. Dimension reduction for estimation of large covariance matrices is achieved by imposing a factor structure with time-varying conditional factor loadings. Statistical properties of the model, including conditions that ensure covariance stationary or returns, are established. The model is applied to modeling the conditional covariance data of large U.S. financial institutions during the financial crisis, where empirical results show that the new model has both superior in- and out-of-sample properties. We show that the superior performance applies to a wide range of quantities of interest, including volatilities, covolatilities, betas and scenario-based risk measures, where the model's performance is particularly strong at short forecast horizons.

A flexible observed factor model with separate dynamics for the factor volatilities and their correlation matrix

In this article, we consider a novel regression model with observed factors. To allow for the prediction of future observations, we model the observed factors using a flexible multivariate stochastic volatility (MSV) structure with separate dynamics for the volatilities and the correlation matrix. The correlation matrix of the factors is time varying, and its evolution is described by an inverse Wishart process. We develop an estimation procedure based on Bayesian Markov chain Monte Carlo methods, which has two major advantages compared to existing methods for similar models in the literature. First, the procedure is computationally more efficient. Second, it can be applied to calculate the predictive distributions for future observations. We compare the proposed model with other multivariate volatility models using Fama-French factors and portfolio weighted return data. The result shows that our model has better predictive performance.

Macroeconomic news surprises and volatility spillover in foreign exchange markets

This paper examines the link between exchange rate volatility and economic fundamentals. In the framework of a multivariate volatility model that allows for volatility spillover, we develop a new impulse response analysis to estimate and decompose the simultaneous effect of macroeconomic news surprises on the foreign exchange volatility. We show that news announcement effects include two components; a direct and an indirect effect induced by volatility spillover. We show that more than 50% of the total accumulated news effect on the Pound and the Yen are due to volatility transmission from the two major currencies and mainly from the Euro.

The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options

We assess the predictive accuracies of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set of 444 multivariate models that differ in their specification of the conditional variance, conditional correlation, innovation distribution, and estimation approach. All of the models belong to the dynamic conditional correlation class, which is particularly suitable because it allows consistent estimations of the risk neutral dynamics with a manageable amount of computational effort for relatively large scale problems. It turns out that increasing the sophistication in the marginal variance processes (i.e., nonlinearity, asymmetry and component structure) leads to important gains in pricing accuracy. Enriching the model with more complex existing correlation specifications does not improve the performance significantly. Estimating the standard dynamic conditional correlation model by composite likelihood, in order to take into account potential biases in the parameter estimates, generates only slightly better results. To enhance this poor performance of correlation models, we propose a new model that allows for correlation spillovers without too many parameters. This model performs about 60% better than the existing correlation models we consider. Relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a more minor way. In addition to investigating the value of model sophistication in terms of dollar losses directly, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performances.

Multivariate rotated ARCH models

This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to fit them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. This yields the rotated BEKK (RBEKK) model. The extension to DCC-type parameterizations is given, introducing the rotated DCC (RDCC) model. Inference for these models is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on the DJIA stocks.

Modelling the Riskiness in Country Risk Ratings

This book presents an econometric analysis of riskiness in country risk ratings. Country risk and its associated risk ratings for 120 countries covering eight geographic regions is analysed by using the univariate and multivariate volatility models.

Orthogonal Transformation of Coordinates in Copula M-GARCH Models - Bayesian Analysis for WIG20 Spot and Futures Returns

We check the empirical importance of some generalisations of the conditional distribution in M-GARCH case. A copula M-GARCH model with coordinate free conditional distribution is considered, as a continuation of research concerning specification of the conditional distribution in multivariate volatility models, see Pipien (2007) and (2010). The main advantage of the proposed family of probability distributions is that the coordinate axes, along which heavy tails and symmetry can be modelled, are subject to statistical inference. Along a set of specified coordinates, both linear and nonlinear dependence can be expressed in a decomposed form.In the empirical part of the paper we considered a problem of modelling the dynamics of the returns on the spot and future quotations of the WIG20 index from the Warsaw Stock Exchange. On the basis of the posterior odds ratio we checked the data support of considered generalisation, comparing it with BEKK model with the conditional distribution simply constructed as a product of the univariate skewed components. Our example clearly showed the empirical importance of the proposed class of the coordinate free conditional distributions.

Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online.