Conditional correlations and volatility spillovers between crude oil and stock index returns

This paper investigates the conditional correlations and volatility spillovers between the crude oil and financial markets, based on crude oil returns and stock index returns. Daily returns from 2 January 1998 to 4 November 2009 of the crude oil spot, forward and futures prices from the WTI and Brent markets, and the FTSE100, NYSE, Dow Jones and S&P500 stock index returns, are analysed using the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), VARMA-AGARCH model of McAleer, Hoti, and Chan (2008), and DCC model of Engle (2002). Based on the CCC model, the estimates of conditional correlations for returns across markets are very low, and some are not statistically significant, which means the conditional shocks are correlated only in the same market and not across markets. However, the DCC estimates of the conditional correlations are always significant. This result makes it clear that the assumption of constant conditional correlations is not supported empirically. Surprisingly, the empirical results from the VARMA-GARCH and VARMA-AGARCH models provide little evidence of volatility spillovers between the crude oil and financial markets. The evidence of asymmetric effects of negative and positive shocks of equal magnitude on the conditional variances suggests that VARMA-AGARCH is superior to VARMA-GARCH and CCC.     

Stock returns and volatility: Evidence from the Athens Stock market index

This paper investigates the volatility of the Athens Stock excess stock returns over the period 1990–1999 through the comparison of various conditional hetero-skedasticity models. The empirical results indicate that there is significant evidence for asymmetry in stock returns, which is captured by a quadratic GARCH specification model, while there is strong persistence of shocks into volatility.     

Modeling and forecasting trading volume index: GARCH versus TGARCH approach

Volatility has been described as an indicator of uncertainty which has implications for investment decisions, risk management as well as monetary policy. This paper investigates the pattern of volatility in the daily trading volume index of Hong Kong stock exchange. The empirical evidence provided in this paper suggests that TGARCH specification is superior to GARCH specification. This is particularly important when one is dealing with the case of asymmetric information that captures the leverage effect of the volatile stock market.     

Multimodality in GARCH regression models

It is shown empirically that mixed autoregressive moving average regression models with generalized autoregressive conditional heteroskedasticity (Reg-ARMA-GARCH models) can have multimodality in the likelihood that is caused by a dummy variable in the conditional mean. Maximum likelihood estimates at the local and global modes are investigated and turn out to be qualitatively different, leading to different model-based forecast intervals. In the simpler GARCH(p,q) regression model, we derive analytical conditions for bimodality of the corresponding likelihood. In that case, the likelihood is symmetrical around a local minimum. We propose a solution to avoid this bimodality.     

Option pricing with stochastic volatility models

A general class of models for derivative pricing with stochastic volatility is analyzed. We include the possibility of jumps for the paths of the asset's price and for those of its volatility. We also consider the case of correlation between the process of the asset's price and that of its volatility. In this way we are able to give a unifying view on most of the models studied in the literature. We will examine theoretical issues related to the market price of volatility risk, the equivalent martingale measures and the possibility of obtaining a numerically tractable formula for contingent claim pricing. Finally, we propose some methodologies to test the behavior of stochastic volatility models when applied to market data.     

Estimating overnight volatility of asset returns by using the generalized dynamic factor model approach

This paper proposes a new approach to estimate the overnight volatility of an individual stock return. Since markets generally do not trade during the overnight period, measures of realized volatility cannot be computed on a “high-frequency” basis. Some studies have resorted to using the square overnight return as a proxy for the overnight realized volatility, but this measure is typically very noisy. The new estimator of the overnight volatility proposed is obtained using the generalized dynamic factor model. The performance of the new proxy is examined using simulated data. This is found to perform better than the squared overnight return. Empirical analysis of the S&P100 constituents confirms the potential of this proxy.     

Risk-parameter estimation in volatility models

This paper introduces the concept of risk parameter in conditional volatility models of the form _?t=_σt(_θ0)_ηt${?}_t={\sigma }_t\left({\theta }_0\right){\eta }_t$ and develops statistical procedures to estimate this parameter. For a given risk measure r$r$, the risk parameter is expressed as a function of the volatility coefficients _θ0${\theta }_0$ and the risk, r(_ηt)$r\left({\eta }_t\right)$, of the innovation process. A two-step method is proposed to successively estimate these quantities. An alternative one-step approach, relying on a reparameterization of the model and the use of a non Gaussian QML, is proposed. Asymptotic results are established for smooth risk measures, as well as for the Value-at-Risk (VaR). Asymptotic comparisons of the two approaches for VaR estimation suggest a superiority of the one-step method when the innovations are heavy-tailed. For standard GARCH models, the comparison only depends on characteristics of the innovations distribution, not on the volatility parameters. Monte-Carlo experiments and an empirical study illustrate the superiority of the one-step approach for financial series.     

Variance-Gamma and Normal-Inverse Gaussian models: Goodness-of-fit to Chinese high-frequency index returns

In this study Variance-Gamma (VG) and Normal-Inverse Gaussian (NIG) distributions are compared with the benchmark of generalized hyperbolic distribution in terms of their fit to the empirical distribution of high-frequency stock market index returns in China. First, we estimate the considered models in a Markov regime switching framework for the identification of different volatility regimes. Second, the goodness-of-fit results are compared at different time scales of log-returns. Third, the goodness-of-fit results are validated through bootstrapping experiments. Our results show that as the time scale of log-returns decrease NIG model outperforms the VG model consistently and the difference between the goodness-of-fit statistics increase. For high-frequency Chinese index returns, NIG model is more robust and provides a better fit to the empirical distributions of returns at different time scales.     

Threshold arch models and asymmetries in volatility

This paper attempts to enlarge the class of Threshold Heteroscedastic Models (TARCH) introduced by Zakoían (1991a). We show that it is possible to relax the positivity constraints on the parameters of the conditional variance. Unconstrained models provide a greater generality of the paths allowing for nonlinearities in the volatility. Cyclical behaviour is permitted as well as different relative impacts of positive and negative shocks on volatility, depending on their size. We give empirical evidence using French stock returns.     

Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations

ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed innovations, we characterize the limiting distribution of an estimator of the conditional value-at-risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal approximation method and the data tilting method, for constructing confidence intervals for the conditional VaR estimator and assess their accuracies by simulation studies. Finally, we apply the proposed approach to an energy market data set.     

Forecasting risk with Markov-switching GARCH models:A large-scale performance study

We perform a large-scale empirical study in order to compare the forecasting performances of single-regime and Markov-switching $\text{GARCH}$ ($\text{MSGARCH}$) models from a risk management perspective. We find that $\text{MSGARCH}$ models yield more accurate Value-at-Risk, expected shortfall, and left-tail distribution forecasts than their single-regime counterparts for daily, weekly, and ten-day equity log-returns. Also, our results indicate that accounting for parameter uncertainty improves the left-tail predictions, independently of the inclusion of the Markov-switching mechanism.     

Modeling share returns - an empirical study on the Variance Gamma model

Due to the fact that there has been only little research on some essential issues of the Variance Gamma (VG) process, we have recognized a gap in literature as to the performance of the various estimation methods for modeling empirical share returns. While some papers present only few estimated parameters for a very small, selected empirical database, Finaly and Seneta (Int Stat Rev 76:167–186, 2008) compare most of the possible estimation methods using simulated data. In contrast to Finaly and Seneta (2008) we utilize a broad, daily, and empirical data set consisting of the stocks of each company listed on the DOW JONES over the period from 1991 to 2011. We also apply a regime switching model in order to identify normal and turbulent times within our data set and fit the VG process to the data in the respective period. We find out that the VG process parameters vary over time, and in accordance with the regime switching model, we recognize significantly increasing fitting rates which are due to the chosen periods.     

Testing for unit roots in time series models with non-stationary volatility

Many of the key macro-economic and financial variables in developed economies are characterized by permanent volatility shifts. It is known that conventional unit root tests are potentially unreliable in the presence of such behaviour, depending on a particular function (the variance profile) of the underlying volatility process. Somewhat surprisingly then, very little work has been undertaken to develop unit root tests which are robust to the presence of permanent volatility shifts. In this paper we fill this gap in the literature by proposing tests which are valid in the presence of a quite general class of permanent variance changes which includes single and multiple (abrupt and smooth-transition) volatility change processes as special cases. Our solution uses numerical methods to simulate the asymptotic null distribution of the statistics based on a consistent estimate of the variance profile which we also develop. The practitioner is not required to specify a parametric model for volatility. An empirical illustration using producer price inflation series from the Stock–Watson database is reported.     

Moving average stochastic volatility models with application to inflation forecast

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical application involving US inflation we find that these moving average stochastic volatility models provide better in-sample fitness and out-of-sample forecast performance than the standard variants with only stochastic volatility.     

Mean-variance hedging for interest rate models¶with stochastic volatility

The mean-variance hedging approach for pricing and hedging claims in incomplete markets was originally introduced for risky assets. The aim of this paper is to apply this approach to interest rate models in the presence of stochastic volatility, seen as a consequence of incomplete information. We fix a finite number of bonds such that the volatility matrix is invertible and provide an explicit formula for the density of the variance-optimal measure which is independent of the chosen times of maturity. Finally, we compute the mean-variance hedging strategy for a caplet and compare it with the optimal stategy according to the local risk minimizing approach. Received: 14 July 2000 / Accepted: 10 April 2001     

Modeling nonresponse in multiwave panel studies using discrete-time Markov models

Quality & Quantity - Nonresponse is of major concern to social scientists, due to the possibility of selectivity: not all groups in the population are equally represented in the final sample,...     

Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension of the parameter space is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian for a variety of multivariate GARCH models including the Vec and BEKK specifications as well as the recent dynamic conditional correlation model. By means of a Monte Carlo investigation of the BEKK–GARCH model we illustrate that employing analytical derivatives for inference is clearly preferable to numerical methods.     

The uncertainty in extreme risk forecasts from covariate-augmented volatility models

For a GARCH-type volatility model with covariates, we derive asymptotically valid forecast intervals for risk measures, such as the Value-at-Risk or Expected Shortfall. To forecast these, we use estimators from extreme value theory. In the volatility model, we allow for leverage effects and the inclusion of exogenous variables, e.g., volatility indices or high-frequency volatility measures. In simulations, we find coverage of the forecast intervals to be adequate for sufficiently extreme risk levels and sufficiently large samples, which is consistent with theory. Finally, we investigate if covariate information from volatility indices or high-frequency data improves risk forecasts for major US stock indices. While—in our framework—volatility indices appear to be helpful in this regard, intra-day data are not.     

The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.