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The purpose of this paper is to show that multivariate t-distribution assumption provides a better description of stock return data than multivariate normality assumption.

The EM algorithm is applied to solve the statistical estimation problem almost analytically, and the asymptotic theory is provided for inference.

The authors find that the multivariate normality assumption is almost always rejected by real stock return data, while the multivariate t-distribution assumption can often be adequate. Conclusions under normality vs under t can be drastically different for estimating expected returns and Jensen’s αs, and for testing asset pricing models.

The results provide improved estimates of cost of capital and asset moment parameters that are useful for corporate project evaluation and portfolio management.

The authors proposed new procedures that makes it easy to use a multivariate t-distribution, which models well the data, as a simple and viable alternative in practice to examine the robustness of many existing results.

Portfolio credit derivatives, such as basket credit default swaps (basket CDS), require for their pricing an estimation of the dependence structure of defaults, which is known to exhibit tail dependence as reflected in observed default contagion. A popular model with this property is the (Student's) t-copula; unfortunately there is no fast method to calibrate the degree of freedom parameter.

In this paper, within the framework of Schönbucher's copula-based trigger-variable model for basket CDS pricing, we propose instead to calibrate the full multivariate t distribution. We describe a version of the expectation-maximization algorithm that provides very fast calibration speeds compared to the current copula-based alternatives.

The algorithm generalizes easily to the more flexible skewed t distributions. To our knowledge, we are the first to use the skewed t distribution in this context.

This paper aims to investigate how effectively the value at risk (VaR) estimated using the student‐t distribution captures the market risk.

Two alternative VaR models, VaR‐t and VaR‐x models, are presented and compared with the benchmark model (VaR‐n model). In this study, we consider the Student‐t distribution as a fit to the empirical distribution for estimating the VaR measure, namely, VaR‐t method. Since the Student‐t distribution is criticized for its inability to capture the asymmetry of distribution of asset returns, we use the extreme value theory (EVT)‐based model, VaR‐x model, to take into account the asymmetry of distribution of asset returns. In addition, two different approaches, excess‐kurtosis and tail‐index techniques, for determining the degrees of freedom of the Student‐t distribution in VaR estimation are introduced.

The main finding of the study is that using the student‐t distribution for estimating VaR can improve the VaR estimation and offer accurate VaR estimates, particularly when tail index technique is used to determine the degrees of freedom and the confidence level exceeds 98.5 percent.

The main value is to demonstrate in detail how well the student‐t distribution behaves in estimating VaR measure for stock market index. Moreover, this study illustrates the easy process for determining the degrees of freedom of the student‐t, which is required in VaR estimation.

The aim of this paper is to compare the performance of VaR (value-at-risk) using Realized Volatility Models (which use intraday returns) with VaR the performance of GARCH-type Models (which use daily returns) with three different distribution innovations (normal distribution, t-distribution, skewed t-distribution). In this paper, we empirically examine VaR forecast of korean stock market using KOSPI and KOSDAQ. Empirical results indicate that the Realized Volatility models is superior to the GARCH-type models in forecasting VaR. We also find Var forecast by skewed t-distribution model are more accurate than those using the normal and t-distribution models. Thus, VaR using Realized Volatility models and skewed t-distribution enhances the performance of risk management in Korean financial markets.

The normal error distribution for the observations and log-volatilities in a stochastic volatility (SV) model is replaced by the Student-t distribution for robustness consideration. The model is then called the t-t SV model throughout this paper. The objectives of the paper are twofold. First, we introduce the scale mixtures of uniform (SMU) and the scale mixtures of normal (SMN) representations to the Student-t density and show that the setup of a Gibbs sampler for the t-t SV model can be simplified. For example, the full conditional distribution of the log-volatilities has a truncated normal distribution that enables an efficient Gibbs sampling algorithm. These representations also provide a means for outlier diagnostics. Second, we consider the so-called t SV model with leverage where the observations and log-volatilities follow a bivariate t distribution. Returns on exchange rates of Australian dollar to 10 major currencies are fitted by the t-t SV model and the t SV model with leverage, respectively.

The purpose of this paper is to investigate how the selection of return distribution impacts estimated volatility in China’s stock market.

The authors use a Bayesian analysis of fat-tailed stochastic volatility (SV) model with Student’s t-distribution, and conduct an out-of-sample test with realized volatility.

Empirical analysis results indicate that fat-tailed SV model performs better in capturing the dynamics of daily returns. The authors find that asymmetry, holiday and day of the week effects are detected in estimated volatility. However, the out-of-sample comparison shows that fat-tailed SV models fail to outperform SV models with normal distribution in fitting and predicting realized volatility.

The contribution of this paper to existing literature is twofold. First, it proves that fat-tailed SV models with Student’s t-distribution perform better than normally distributed SV models in fitting daily returns of China’s stock market. Second, this paper takes asymmetry, holiday and day of the week effects into consideration at the same time in the fat-tailed SV model.

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Bangladesh foreign exchange rate index from January 1999 to December 31, 2012. The return series of Bangladesh foreign exchange rate are leptokurtic, significant skewness, deviation from normality as well as the returns series are volatility clustering as well. We found that student t distribution into GARCH model improves the better performance to forecast the volatility for Bangladesh foreign exchange market. The traditional likelihood comparison showed that the importance of GARCH model in modeling of Bangladesh foreign market, but the modern nonparametric specification test found that RW, AR and the model with GARCH effect are still grossly mis-specified. All these imply that there is still a long way before we reach the adequate specification for Bangladesh exchange rate dynamics.

The purpose of this paper is to describe a generalization of the familiar two‐sample t‐test for equality of means to the case where the sample values are to be given unequal weights. This is a natural situation in financial risk modeling when some samples are considered more reliable than others in predicting a common mean. We also describe an example with real credit data showing that ignoring this modification of the two‐sample test can lead to the wrong statistical conclusion.

We follow the analysis of the classical two‐sample tests in the more general situation of weighted means. We also test our methods against some market data to assess the importance of the findings.

We formulate some explicit test statistics that should be used when the sample values are to be assigned differing known weights. Different cases are presented depending on how much is known about the variances. In the most typical case (the unpooled two‐sample test), we approximate the test statistic with a t‐distribution. Proofs are given where possible.

In the unpooled case, we still only have an approximate t‐distribution. This is related to the classical Behrens‐Fisher problem, which is still not fully solved. We also focus on the case where the sample values are normally distributed. It would be valuable to see how far the discussion can be extended to non‐normal distributions.

Researchers should use the two‐sample test statistics given in this paper instead of the standard ones when testing for equality of weighted means.

Weighted means occur frequently in situations when the credibility or reliability of data vary. However, standard tests for equality of means do not take weights into account. These results will be of value to any researchers studying statistical means of data of varying reliability, such as corporate bond spreads.

The paper aims to investigate the relative performance of the most popular value‐at‐risk (VaR) estimates with an emphasis on the extreme value theory (EVT) methodology for seven Middle East and North Africa (MENA) countries.

The paper calculates tails distributions of return series by EVT. This allows computing VaR and comparing the results with Variance‐Covariance method, Historical simulation, and ARCH‐type process with normal distribution, Student‐t distribution and skewed Student‐t distribution. The paper assesses the performance of the models, which are used in VaR estimations, based on their empirical failure rates.

The empirical results demonstrate that the return distributions of the MENA markets are characterized by fat tails which implies that VaR measures relies on the normal distribution will underestimate VaR. The results suggest that the extreme value approach, by modeling the tails of the return distributions, are more relevant to measure VaR in most of the MENA.

The results show that the use of conventional methodologies such as the normal distribution model to estimate the financial market risk in MENA countries may lead to faulty estimation of risk in the world of volatile markets.

The paper tried to fill the gap in the literature and perform an evaluation of the relative performance of the most popular VaR estimates with an emphasis on the EVT methodology in seven MENA emerging stock markets. A comparison of the performance between EVT and other VaR techniques should support the decision whether more or less sophisticated methods are appropriate in order to assess stock market risks in the MENA countries.

This paper aims to investigate the volatility transmission and dynamics in China Securities Index (CSI) 300 index futures market.

This paper applies the bivariate Constant Conditional Correlation (CCC) and Dynamic Conditional Correlation (DCC) Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models using high frequency data. Estimates for the bivariate GARCH models are obtained by maximising the log-likelihood of the probability density function of a conditional Student’s t distribution.

This empirical analysis yields a few interesting results: there is a one-way feedback of volatility transmission from the CSI 300 index futures to spot returns, suggesting index futures market leads the spot market; volatility response to past bad news is asymmetric for both markets; volatility can be intensified by the disequilibrium between spot and futures prices; and trading volume has significant impact on volatility for both markets. These results reveal new evidence on the informational efficiency of the CSI 300 index futures market compared to earlier studies.

This paper shows that the CSI 300 index futures market has improved in terms of price discovery one year after its existence compared to its early days. This is an important finding for market participants and regulators. Further, this study considers the volatility response to news, market disequilibrium and trading volume. The findings are thus useful for financial risk management.