Probability Integrals of the Multivariate t Distribution

Results on probability integrals of multivariate t distributions are reviewed. The results discussed include: Dunnett and Sobel's probability integrals, Gupta and Sobel's probability integrals, John's probability integrals, Amos and Bulgren's probability integrals, Steffens' non‐central probabilities, Dutt's probability integrals, Amos' probability integral, Fujikoshi's probability integrals, probabilities of cone, probabilities of convex polyhedra, probabilities of linear inequalities, maximum probability content, and Monte Carlo evaluation.     

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.     

Global and regional integration of the Middle East and North African (MENA) stock markets

We investigate financial integration of MENA region to facilitate a more in-depth exploration of the structure of interdependence and transmission mechanism of stock returns and volatility between MENA and world stock markets. The EGARCH-M models with a generalized error distribution are employed to consider both leverage effect of negative shocks and leptokurtosis prevalent in the MENA stock markets. The estimation results of multivariate AR-GARCH models indicate that there are large and predominantly positive volatility spillovers and volatility persistence in conditional volatility between MENA and world stock markets. Own-volatility spillovers are generally higher than cross-volatility spillovers for all the markets.     

Stochastic comparisons of multivariate reversed frailty model

Multivariate frailty approaches are most commonly used to define distributions of random vectors, which represent lifetimes of individuals or components and stochastically compare them in terms of various multivariate orders. In this paper, we study a multivariate shared reversed frailty model and a general multivariate reversed frailty mixture model, and derive sufficient conditions for some of the stochastic orderings to hold among the random vectors. We also consider a particular case of a general multivariate mixture model in which the baseline distribution function is represented in terms of a copula and study stochastic comparisons (stochastic and lower orthant order) among the two random vectors.     

Extreme dependence in price transmission analysis

We propose a generalized procedure that combines conventional price transmission analysis with copula-based dynamic tail dependence, to examine price relationships under extreme conditions. This approach is used to examine Ukrainian wheat markets where export restrictions combined with price surges, 2006–2008 and 2010–2012, have contributed to a turbulent market. The results indicate that domestic prices were effectively insulated from world price shocks, but that a ‘rocket and feathers’ price relation held between domestic flour and wheat prices. These asymmetric price co-movements changed with the degree of restrictiveness of the export prohibitions.     

Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals

In this paper we study the existence of arbitrage opportunities in a multi-asset market when risk-neutral marginal distributions of asset prices are known. We first propose an intuitive characterization of the absence of arbitrage opportunities in terms of copula functions. We then address the problem of detecting the presence of arbitrage by formalizing its resolution in two distinct ways that are both suitable for the use of optimization algorithms. The first method is valid in the general multivariate case and is based on Bernstein copulas that are dense in the set of all copula functions. The second one is easier to work with but is only valid in the bivariate case. It relies on results about improved Fréchet–Hoeffding bounds in presence of additional information. For both methods, details of implementation steps and empirical applications are provided.     

Gender differences,physical activity and body weight

We investigate the effect of physical activity on bodyweight and the gender differences in such effects, following the copula approach to endogenous switching regression. Using data from the 2006 Behavioral Risk Factor Surveillance System (BRFSS), we find differentiated effects of socio-demographic variables on exercise and on Body Mass Indexes (BMIs), and differentiated effects of exercise on BMI, between genders. Regular exercise, on average, decreases BMI by 1.78 for women and 1.01 for men. Food price away from home has negative effects on BMI of both men and women.     

Dependence structure between nominal and index-linked bond returns: a bivariate copula and DCC-GARCH approach

This article investigates the dependence structure related to four French nominal and index-linked bonds with various maturities and reference indices. To achieve this aim, we estimate various copulas to select the appropriate one for our data. We also compare results obtained using the copula method with multivariate dynamic conditional correlation GARCH (DCC-GARCH) modelling. The major issue in this study is that the best copulas used to model the dependence among bond returns are the Plackett and Student models. We also find a dynamic correlation between bond returns. In particular, the relationship between nominal and indexed bonds is characterized by an asymmetric dependence. Moreover, the results obtained by the copula approach are confirmed by those obtained by multivariate GARCH modelling. Our empirical study provides a useful method that may be employed by decision-makers to quantitatively introduce dependence and spillover effects in their bond issuance policy. For investors, we propose optimal investment combinations in bonds with respect to their investment horizons.     

基于Copula的股票市场波动溢出分析

对于动态投资组合与风险管理来说,测定波动溢出效应是非常重要的。已有的研究是建立在不同金融市场之间的波动是线性相关的,而线性相关并不能描述金融市场之间的非线性关系。借用Copula技术来描述股票市场之间的非线性关系、SV模型来刻画股票市场数据的边缘分布,并引入波动变结构论分析判断波动溢出,实证分析验证了方法是可行的。     

Return Dependence and the Limits of Product Diversification in Financial Firms

Copula‐GARCH models indicate dependence between bank returns and those to insurance underwriting, securities brokerage, and mortgage finance increased during the recent crisis. In contrast, dependence between banks and the broader market was little changed. The crisis‐related jump in return dependence within the financial services sector was greatest for banks that had previously appeared the most independent. Larger banks were also especially prone to increased dependence. These findings raise doubts about the ability of financial conglomerates to diversify effectively and highlight the need for policy progress in methods for resolving such institutions should they become illiquid or insolvent.