Multivariate GARCH Research Articles

Multivariate Asymmetric GARCH Model with Dynamic Correlation Matrix

This study examines the problem of modeling the joint dynamics of conditional volatility of several financial assets under an asymmetric relationship between volatility and shocks in returns (leverage effect). We propose a new multivariate asymmetric conditional heteroskedasticity model with a dynamic conditional correlation matrix (DCC-EGARCH). The proposed method allows modelling the joint dynamics of several financial assets taking into account the leverage effect in the financial markets. DCC-EGARCH model has two main advantages over previously proposed multivariate asymmetric specifications. It involves a substantially simpler optimization problem and does away with the assumption of conditional correlation time invariance. These features make the model more suitable for practical applications. To study the properties of the obtained estimators, we conducted a simulated data analysis. As a result, we found statistical evidence in favor of the developed DCC-EGARCH model compared with the symmetric DCC-GARCH process in case of considering data with the presence of the leverage effect. Further, we applied the proposed method to analyze the joint volatility of Rosneft stock returns and Brent oil prices. By estimating the DCC-EGARCH model, we found statistical evidence for both the presence of the leverage effect in the oil price data and the presence of the dynamic correlation structure between the time series, which motivates the practical application of the proposed method.

Following the leaders? A study of co-movement and volatility spillover in BRICS currencies

The paper investigates return co-movement and volatility spillover among the currencies of Brazil, Russia, India, China, and South Africa (the BRICS member countries) and four major developed countries from April 2006 to October 2019. Using Bloomberg daily data on exchange rates, the study employs a flexible multivariate generalized autoregressive conditional heteroskedasticity (MGARCH)–dynamic conditional correlation (DCC) model and a vector autoregressive (VAR)–based spillover index, as the empirical strategy. Along with evidence of exchange rate volatility in BRICS currencies, among which the Russian ruble and the Chinese yuan are explosive, the econometric estimation results show the presence of significant return co-movement and volatility spillover among the foreign exchange markets across different countries. The currency markets in developed countries, as leaders, are found to transmit volatility mostly to BRICS currency markets, which are net receivers. The degree of spillover, however, varies across countries, with Brazil and Russia passing on volatility to the developed countries whereas India, China, and South Africa receive volatility from their developed counterparts.

The linkage between international dairy commodity prices and volatility: a panel-GARCH analysis

PurposeThe study's purpose is to investigate the price volatility of four dairy commodities (skim milk powder [SMP], whole milk powder [WMP], butter and cheddar cheese) in the three most significant regional markets (EU, Oceania and US) in the international dairy market.Design/methodology/approachThe study uses a panel-Generalized Autoregressive Conditional Heteroskedastic (panel-GARCH) modeling technique and data from January 12, 2001, to April 28, 2017.FindingsConditional volatility was higher during subperiods 2007–2010 and 2014–2016 when conditional cross-correlations between prices had the lowest values. In some cases, they were negative (i.e. between the EU and the USA and between Oceania and the USA for both butter and cheese). Interdependence across the three dairy markets, especially for SMP and WMP markets and for the butter market between EU and Oceania is also strongly evidenced. Interdependence is responsible for the spillover of price shocks across the three regions.Research limitations/implicationsThe data set used should be extended to cover the COVID-19 pandemic period.Originality/valueThis is the first study to use panel-GARCH to examine international dairy prices and volatility linkages, where previous studies mainly used multivariate GARCH models. Panel-GARCH allows a high-dimensional data series (i.e. 12 dairy prices) and generates potential efficiency gains in estimating conditional variances and covariances by incorporating information about heterogeneity across markets and considering their interdependence.

Estimating Conditional Correlations among Subgroups of Service Sector in Vietnam Stock Exchanges

The paper explores the time-varying correlations among five subgroups of the service sector i.e., CONSTRUCTION, ENERGY, TECHOLOGY, TRANSPORT and TOURISM, and market index ‘VNINDEX’ in the Vietnam stock exchanges. Two multivariate GARCH models namely the CCC and DCC were employed to examine how closely returns of each pair correlate with each other. The estimates of conditional correlations reveal low to relatively high [0.1958; 0.6720] between the selected indexes, of which the subgroup ‘TECHNOLOGY’ exhibits low correlations with the others, while the remaining subgroups show medium interdependence from each other and relatively high with the market index. Moreover, the estimates of the DCC model show the time-varying patterns in the pair correlation paths among the selected indexes. The findings provide a crucial background for investors, capital investment funds, listed firm owners and market managers in the Vietnam stock exchanges in fore-seeing long-run and short-run investment, portfolio selection and risk management in the selected indexes.

The relationship between global stock and precious metals under Covid-19 and happiness perspectives

In this paper, we examine the relationship between global stock markets, as respectively represented by the FTSE All-World Series and the MSCI Emerging Markets indexes, and the S&P GSCI Precious Metals index from 01 September 1999 to 03 May 2021. We employ the conditional correlation multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) to investigate this stock-precious metals nexus in terms of return and volatility spillovers. The study assesses impacts of the Covid-19 pandemic on the stock-precious metals nexus and further examine this relationship by supplementing the Twitter’s Daily Happiness Sentiment index to the methodological framework for the period from 01 January 2020 to 03 May 2021. We find that precious metals positively influence stock markets before the Covid-19 outbreak and firmly play a valuable role due to their hedge and safe haven characteristics. In contrast, the bivariate GARCH framework does not provide statistically significant evidence on the stock-precious metals nexus during the Covid-19 pandemic. Meanwhile, the tri-variate GARCH approach with stock markets, precious metals, and happiness sentiment indexes reveals sufficiently complicated interactions between these return series. Prominently, past change in the happiness index negatively affects the stock returns but positively drives the performance of precious metals. These findings indirectly demonstrate the stock-precious metals nexus under impacts of the Covid-19 pandemic and reflect the demand of precious metals during crisis periods. Accordingly, we suggest a reasonable method of adjusting the proxies when no interaction effect is significantly found during unprecedented outbreaks.

Currency hedging behavior for stock returns uncertainty in Ghana

ABSTRACT This article investigates the dynamic interaction between stock market returns and exchange rate movement and their implication for portfolio risk management in Ghana. To do so, and considering the Covid-19 crisis, the Dynamic Conditional Correlation Multivariate GARCH estimation technique was employed on daily data for Ghana Stock Exchange (GSE) Composite Index and the Ghana Cedi to USD, Euro, and GBP exchange rates from 3 January 2012 to 26 November 2021. The results revealed that: (i) the GSE market has no significant exposure to the USD, Euro, and GBP exchange rates in the full sample and periods before the crisis but was significantly exposed to the Euro rates during the crisis, (ii) the returns on holding foreign currencies were relatively higher but riskier compared to returns on stocks for the full sample and periods before the crisis, and (iii) while the Euro rates act as the most efficient hedge currency for stock returns uncertainty the correlations between stock returns and exchange rate movement were generally low and therefore, forming a portfolio of stocks and currency pairs improved an investor’s daily returns and risk. Based on the findings, relevant policy suggestions are offered to guide investors and policymakers.

Commodity financialization and funding liquidity in China

This study examines commodity financialization in China through commodity futures and stock market price co-movement, captured by a dynamic conditional correlation multivariate GARCH model (DCC-MGARCH). We find a dramatic increase in correlation after 2004; however, after 2010, the correlation decreases. We further investigate how funding liquidity affectes commodity financialization and find that its effect on the industrial sector is stronger than that on the agricultural sector, which reflects commodity financialization layering.

IMPACT OF COVID-19 ON VOLATILITY SPILLOVERS ACROSS INTERNATIONAL MARKETS: EVIDENCE FROM VAR ASYMMETRIC BEKK GARCH MODEL

This study contributes to the COVID-19 related literature in finance by examining asymmetric volatility spillover across stock, Bitcoin, gold and oil markets before and during the COVID-19 pandemic. Based on multivariate VAR asymmetric BEKK GARCH model, findings show that the interdependency across the examined markets intensified during the recent health crisis. Moreover, we find that oil market appears as major receivers of volatility spillovers, particularly from gold and stock market which is mostly the results of dramatic collapse of oil prices during the COVID-19 outbreak. We also document that gold exhibits a strong resilience during COVID-19 crisis, suggesting its potential hedging ability during uncertainty. As for asymmetric volatility spillover, findings show the highest sensitivity of oil and Bitcoin markets to gold and US stock markets. Our findings have important implications for investors, portfolio managers and policymakers.

Return and volatility spillovers between Chinese and U.S. clean energy related stocks

This paper aims to empirically investigate the dynamic connectedness between oil prices and stock returns of clean energy-related and technology companies in China and U.S. financial markets. We apply three multivariate GARCH model specifications (CCC, DCC and ADCC) to investigate the return and volatility spillovers among price and return series. We use rolling window analysis to forecast out-of-sample one-step-ahead dynamic conditional correlations and time-varying optimal hedge ratios. Our results suggest that Invesco China Technology ETF (CQQQ) is the best asset to hedge Chinese clean energy stocks followed by WTI, ECO, and PSE. Our results are reasonably robust to the choice of different model refits and forecast length of rolling window analysis. Our empirical findings provide investors and policymakers with the systematic understanding of return and volatility connectedness between China and U.S. clean energy stock markets.

Testing Financial Contagion in Emerging Countries: Evidence From BRICS Countries

This study uses a Multivariate Generalised Autoregressive Conditional Heteroskedasticity (MGARCH) model to examine the pure form of financial contagion in BRICS countries (Brazil, Russia, India, China, and South Africa) in the wake of two major international financial crises namely the U.S. sub-prime and Eurozone sovereign debt crises (EZDC). The pure form of contagion refers to the spread of shocks that are unrelated to macroeconomic fundamentals and are simply the product of irrational phenomena like panics, herd behaviour, loss of confidence, and risk aversion. To investigate contagion the present study analyses the pairwise dynamic cross-correlation between the US and Eurozone equity markets as ‘source’ (ground zero) markets and individual BRICS stock markets as ‘target’ markets.For the each of the two crises that are examined the sets of data used, were divided into two sub-periods (1) the crisis period and (2) the stable period. For the Sub-prime crisis, the findings of the present study indicate the presence of cross-conditional volatility between the US and BRICS stock markets. The results also showed that the cross-conditional volatility coefficient is high in magnitude during periods of financial upheaval compared to a tranquil period, hence the conclusion that there was financial contagion during in BRICs stock markets (except in Chinese market) following the U.S. sub-prime crisis. As for the EZDC, equity markets in Brazil, India and China seemed to react equally (in both the ‘crisis’ and ‘post-crisis’ periods) from shocks emanating from European equity market. Hence the conclusion that there was no contagion in Brazil, India and China following the Eurozone sovereign debt crisis.

Exchange rate spillover effect on Stock Returns: Evidence from Pakistan

Volatility spillover is measured as the transferal of variability among different financial markets. The objective of this study is to see if there is any effect volatility spillover amongexchange rates and stock returns in Pakistan or not. For this purpose the secondary dataranging from April 2010 – April 2020 is collected and analyzed using multivariate dynamic conditional correlation GARCH (DCC-MGARCH) model. It is observed that there is a notable volatility spillover impact between the two. This study can be used by different investing firms and individual investors incorporating the spillover impact in order to hedge and diversify their portfolios. It can also be used by educational institutions for teaching and training purposes. It can also help the policy makers providing recommendations regarding spillover effect between the concerned markets.

Volatility spillovers: A sparse multivariate GARCH approach with an application to commodity markets

AbstractWe propose sparse DCC‐GARCH and BEKK‐GARCH models based on regularization. We use the models to study daily return volatility and correlation spillovers for the 24 constituents of the Bloomberg commodity index in the period 2000–2018. The sparse models outperform the diagonal models out‐of‐sample in terms of model fit and other criteria. We also test whether the higher visibility of metals and energy markets compared with agricultural commodities affects the speed of information processing. We find correlation spillovers from metals and energy to agricultural commodities even though the latter tend to settle somewhat later.

Large dynamic covariance matrices: Enhancements based on intraday data

Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how performance can be increased further by using open/high/low/close (OHLC) price data instead of simply using daily returns. A key innovation, for the improved modeling of not only dynamic variances but also of dynamic correlations, is the concept of a regularized return, obtained from a volatility proxy in conjunction with a smoothed sign of the observed return.

The link between regional CDS spreads and equity returns: a multivariate GARCH approach

The link between regional CDS spreads and equity returns: a multivariate GARCH approach

Multivariate Hyper-Rotated GARCH-BEKK

Abstract For large multivariate models of generalized autoregressive conditional heteroskedasticity (GARCH), it is important to reduce the number of parameters to cope with the ‘curse of dimensionality’. Recently, Laurent, Rombouts and Violante (2014 “Multivariate Rotated ARCH Models” Journal of Econometrics 179: 16–30) developed the rotated multivariate GARCH model, which focuses on the parameters for standardized variables. This paper extends the rotated multivariate GARCH model by considering a hyper-rotation, which uses a more flexible structure for the rotation matrix. The paper shows an alternative representation based on a random coefficient vector autoregressive and moving-average (VARMA) process, and provides the regularity conditions for the consistency and asymptotic normality of the quasi-maximum likelihood (QML) estimator for VARMA with hyper-rotated multivariate GARCH. The paper investigates the finite sample properties of the QML estimator for the new model. Empirical results for four exchange rate returns show the new specifications works satisfactory for reducing the number of parameters.

Searching for hedging and safe haven assets for Indian equity market – a comparison between gold, cryptocurrency and commodities

PurposeThis paper aims to evaluate the hedging and safe haven properties of gold, cryptocurrency and commodities against the Indian equity market.Design/methodology/approachFirst, the authors estimate the hedging and safe haven abilities of gold, cryptocurrency and commodities for the Indian stock market and further verify whether such properties vary across the broad stock market indices and over the different degrees of market volatility. Second, the authors use the multivariate GARCH framework to calculate the dynamic hedge ratios and hedging efficiencies to compare the hedging properties of the alternative asset classes. Third, the authors verify the robustness of the general findings during the recent crisis emanating from the outbreak of the COVID-19 pandemic.FindingsGold, cryptocurrency and most commodities have significant hedging abilities. Only natural gas, crude oil and aluminum, on the other hand, have safe haven property. Neither gold nor cryptocurrency qualifies as a safe haven asset. On the other hand, the financialization of the Indian commodities market provides a significant dividend to investors in terms of hedging and safe haven capabilities. The authors find the least negative hedge ratio and the highest positive hedging effectiveness for the stock-crude oil and stock-natural gas portfolios. The central observations of the paper remain immune to the COVID crisis.Originality/valueFocusing on the Indian equity market, the paper compares the diversification abilities of traditional assets like gold with those of the modern class of assets, including cryptocurrency and other commodities.

MEASURING CONTAGION BETWEEN ENERGY AND STOCK MARKET DURING FINANCIAL CRISIS: ASYMMETRIC DYNAMICS IN THE CORRELATIONS

This paper deals with the study of the Asymmetric Dynamic Conditional Correlation (ADCC) model developed by Cappiello et al. (2006). The A-DCC models carry out better than the non-asymmetric ones. The methodological design is an appropriate multivariate vector and autoregressive exponential GARCH (M-VAR-EGARCH) process which investigate the nature of the volatility and return spillover mechanism across markets. This article examines the dynamic linkages between the stock market and oil price in the US and the Euro-Zone from January 2, 2004 to July 5, 2013. The findings support the existence of a contagion effect during the Greek debt crisis but not the subprime crisis. The correlations between oil prices and stock return of the financial market reveal a certain degree of interdependence among oil market that is lower during the debt crisis.

Multivariate Overnight GARCH-Ito Model with Applications in Large Volatility Matrix Estimation and Prediction

This paper introduces a unified multivariate overnight GARCH-It\^o model for volatility matrix estimation and prediction both in the low- and high-dimensional set-up. To account for whole-day market dynamics in the financial market, the proposed model has two different instantaneous volatility processes for the open-to-close and close-to-open periods, while each embeds the discrete-time multivariate GARCH model structure. We call it the multivariate overnight GARCH-It\^o (MOGI) model. Based on the connection between the discrete-time model structure and the continuous-time diffusion process, we propose a weighted least squares estimation procedure for estimating model parameters with open-to-close high-frequency and close-to-open low-frequency financial data, and establish its asymptotic theorems. We further discuss the prediction of future vast volatility matrices and study its asymptotic properties. A simulation study is conducted to check the finite sample performance of the proposed estimation and prediction methods. The empirical analysis is carried out to compare the performance of the proposed MOGI model with other benchmark methods in portfolio allocation problems.

Modeling time varying risk of natural resource assets: Implications of climate change

A multivariate GARCH model of natural resources is specified to capture the effects of time varying portfolio risk. A special feature of the model is the inclusion of realized volatility for natural resource assets that are available at multiple frequencies as well as being sensitive to sudden changes in climatic conditions. Natural resource portfolios under climate change are simulated from bootstrapping schemes as well as being derived from global climate model projections. Both approaches are applied to a multiasset water portfolio model consisting of reservoir inflows, rainwater harvesting, and desalinated water. The empirical results show that while reservoirs remain the dominant water asset, adaptation to climate change involves increased contributions from rainwater harvesting and more frequent use of desalinated water. It is estimated that climate change increases annual water supply costs by between 7% and 44% over a 20‐year forecast horizon.

Распространение волатильности между триадой Россия–Индия–Китай и США: многомерный обобщенный авторегрессионный анализ условной гетероскедастичности

This study is concerned with the identification of the economic links and volatility spillover effects between the United States and the Russia–India–China triad from 2010 to 2019. This decade is characterized by a lack of major global financial crises in the economy, although the liberalization of the Chinese stock market and the reciprocal sanctions between Russia and developed countries, followed by the trade wars between the United States and China changed the relationship between stock markets. This study tests three hypotheses. The first hypothesis is associated with the post‑2014 change of interconnection between the Chinese and the Russian and the Indian stock markets. The second hypothesis tests the fact that the Russian market has become less dependent on the US market. The third hypothesis: the trade war between the United States and China increased the volatility spillover effects between financial markets. The multivariate GARCH BEKK model was used for calculations. The research results presented herein can be used to draw conclusions about the general current situation in the world stock markets and their future development trends, as well as for a more complete understanding of the mechanisms of interaction and mutual influence of financial markets for possible diversification of the investment portfolio.