Volatility linkages in the spot and futures market in Australia: a copula approach

To better characterize the dependence structure of the joint returns distribution, we propose to blend copula functions with Asymmetric GARCH (AGARCH) models, which are allowed for generalized error distribution. We model the copula’s marginals by the AGARCH processes that can differentiate between the impacts of positive and negative shocks on the returns volatility while taking the large kurtosis of the returns into account. An application of the procedure is elaborated on the All Ordinaries Index and its corresponding Share Price Index on future contracts in Australia. The findings reveal that the two spot and future markets show a strong right tail dependence but no left tail dependence. This provides a very useful knowledge for the risk management and hedging in futures markets.     

Modeling non-normal corporate bond yield spreads by copula

This research focuses on modeling for how corporate bond yield spreads are affected by explanatory variables such as equity volatility, interest rate volatility, r, slope, rating, liquidity, coupon rate, and maturity. The existing literature assumes normality and linearity in the analysis, which is not the case in our sample. Thus, through a powerful and flexible copula approach, we study the dependence at the mean of the joint distribution by using the Gaussian copula marginal regression method and the dependence structure at the tails by using various copula functions. To our knowledge, this is the first application of the copula marginal regression model to bond market data. In addition, we employ several copula functions to test for the tail dependence between yield spreads and other explanatory variables. We find stronger tail dependence in the joint upper tail for the relation between equity volatility and yield spreads, among others. This result indicates the positive effect of equity volatility on yield spreads in the upper tail is greater than that in the low tail. This finding should be useful to practitioners, such as investors. By relying on better-fitting, more meaningful statistical models, this paper contributes to the extant literature on how corporate bond yield spreads are determined.     

The conditional dependence structure of insurance sector credit default swap indices

This study assesses the dependence structure of insurance sector credit default swap indices, using a copula-GARCH approach. We use daily data of the US, EU, and UK insurance sectors, covering the period from January 2004 to June 2013. We find substantial increases in dependence during the financial crisis periods. Prior to the crises, various copulas are found to best fit each pair; specifically, asymmetric tail dependence is found for the UK–US pair, suggesting the possibility of large simultaneous losses. However, during the crisis periods, the Frank copula fits best, with no significant tail dependence detected, implying low systemic risks.     

Switching generalized autoregressive score copula models with application to systemic risk

Recent financial disasters have emphasized the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme events strongly relies on their flexibility to account for the highly nonlinear and asymmetric dependence patterns observed in financial time series. In this paper, we develop a new class of flexible copula models where the dependence parameters evolve according to a Markov switching generalized autoregressive score (GAS) dynamics. Maximum likelihood estimation is performed using a two‐step procedure where the second step relies on the expectation–maximization algorithm. The proposed switching GAS copula models are then used to estimate the conditional value at risk and the conditional expected shortfall, measuring the impact on an institution of extreme events affecting another institution or the market. The empirical investigation, conducted on a panel of European regional portfolios, reveals that the proposed model is able to explain and predict the evolution of the systemic risk contributions over the period 1999–2015.     

A Simple Estimator of Two-Dimensional Copulas,with Applications1

Copulas are distributions with uniform marginals. Non-parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi-spaced grid a natural starting point. However, the mixed-integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non-parametric MLE of B-spline coefficients on possibly non-equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.     

Dynamic stochastic copula models: estimation,inference and applications

We propose a new dynamic copula model in which the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. We propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula. Parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling. We discuss goodness‐of‐fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, we show that the proposed model outperforms standard competing models. Copyright © 2010 John Wiley & Sons, Ltd.     

A Simple Estimator of Two‐Dimensional Copulas,with Applications1

Copulas are distributions with uniform marginals. Non‐parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi‐spaced grid a natural starting point. However, the mixed‐integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non‐parametric MLE of B‐spline coefficients on possibly non‐equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.     

Improving forecasting performance using covariate-dependent copula models

Copulas provide an attractive approach to the construction of multivariate distributions with flexible marginal distributions and different forms of dependences. Of particular importance in many areas is the possibility of forecasting the tail-dependences explicitly. Most of the available approaches are only able to estimate tail-dependences and correlations via nuisance parameters, and cannot be used for either interpretation or forecasting. We propose a general Bayesian approach for modeling and forecasting tail-dependences and correlations as explicit functions of covariates, with the aim of improving the copula forecasting performance. The proposed covariate-dependent copula model also allows for Bayesian variable selection from among the covariates of the marginal models, as well as the copula density. The copulas that we study include the Joe-Clayton copula, the Clayton copula, the Gumbel copula and the Student’s $t$-copula. Posterior inference is carried out using an efficient MCMC simulation method. Our approach is applied to both simulated data and the S&P 100 and S&P 600 stock indices. The forecasting performance of the proposed approach is compared with those of other modeling strategies based on log predictive scores. A value-at-risk evaluation is also performed for the model comparisons.     

Assessment of time-varying systemic risk in credit default swap indices: Simultaneity and contagiousness

This study assesses systemic risk inherent in credit default swap (CDS) indices using empirical and statistical analyses. We define systemic risk in two perspectives: the possibilities of simultaneous and contagious defaults, and then quantify them separately across benchmark models. To do so, we employ a Marshall-Olkin copula model to measure simultaneous default risk, and an interacting intensity-based model to capture contagious default risk. For an empirical test, we collect daily data for the iTraxx Europe CDS index and its tranche prices in the period from 2005 to 2014, and calibrate model parameters varying across time. In addition, we select forecasting models that have minimal prediction errors for the calibrated time series. Finally, we identify significant changes in each dynamic of systemic risk indicator before and after default and downgrade-related episodes that have occurred in the global financial crisis and European sovereign debt crisis.     

Copula-based multivariate GARCH model with uncorrelated dependent errors

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. The aim of this paper is to model MGARCH for non-normal multivariate distributions using copulas. We model the conditional correlation (by MGARCH) and the remaining dependence (by a copula) separately and simultaneously. We apply this idea to three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle [Engle, R.F., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350], the varying correlation (VC) model of Tse and Tsui [Tse, Y.K., Tsui, A.K., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362], and the BEKK model of Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. Empirical analysis with three foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection and out-of-sample multivariate density forecast, and in terms of these criteria the choice of copula functions is more important than the choice of the volatility models.     

A Skew‐normal copula‐driven GLMM

This paper presents a method for fitting a copula‐driven generalized linear mixed models. For added flexibility, the skew‐normal copula is adopted for fitting. The correlation matrix of the skew‐normal copula is used to capture the dependence structure within units, while the fixed and random effects coefficients are estimated through the mean of the copula. For estimation, a Monte Carlo expectation–maximization algorithm is developed. Simulations are shown alongside a real data example from the Framingham Heart Study.     

Crack spread option pricing with copulas

A copula-based approach for pricing crack spread options is described. Crack spread options are currently priced assuming joint normal distributions of returns and linear dependence. Statistical evidence indicates that these assumptions are at odds with the empirical data. Furthermore, the unique features of energy commodities, such as mean reversion and seasonality, are ignored in standard models. We develop two copula-based crack spread option models using a simulation approach that address these gaps. Our results indicate that the Gumbel copula and standard models (binomial, and Kirk and Aron (1995)) mis-price a crack spread option and that the Clayton model is more appropriate. We contribute to the energy derivatives literature by illustrating the application of copula models to the pricing of a heating oil–crude oil “crack” spread option.     

时变Copula模型的非参数推断

运用Copula模型研究金融变量之间的相关结构,是近年来金融分析中的一个热点,如何估计Copula模型中的时变参数则是一个重点和难点问题。本文从非参数建模思想为切入点,提出经验分布函数—局部极大似然法(ECDF-LML)估计Copula函数中的时变参数,研究了Copula模型参数是否时变的统计假设检验问题。最后通过大量随机模拟研究验证了本文所提出的方法较DCC-MGARCH方法在刻画随机变量动态相关性方面更具优越性且很稳健。     

Modelling dependence using skew t copulas: Bayesian inference and applications

We construct a copula from the skew t distribution of Sahu et al. ( 2003 ). This copula can capture asymmetric and extreme dependence between variables, and is one of the few copulas that can do so and still be used in high dimensions effectively. However, it is difficult to estimate the copula model by maximum likelihood when the multivariate dimension is high, or when some or all of the marginal distributions are discrete‐valued, or when the parameters in the marginal distributions and copula are estimated jointly. We therefore propose a Bayesian approach that overcomes all these problems. The computations are undertaken using a Markov chain Monte Carlo simulation method which exploits the conditionally Gaussian representation of the skew t distribution. We employ the approach in two contemporary econometric studies. The first is the modelling of regional spot prices in the Australian electricity market. Here, we observe complex non‐Gaussian margins and nonlinear inter‐regional dependence. Accurate characterization of this dependence is important for the study of market integration and risk management purposes. The second is the modelling of ordinal exposure measures for 15 major websites. Dependence between websites is important when measuring the impact of multi‐site advertising campaigns. In both cases the skew t copula substantially outperforms symmetric elliptical copula alternatives, demonstrating that the skew t copula is a powerful modelling tool when coupled with Bayesian inference. Copyright © 2010 John Wiley & Sons, Ltd.     

A time-varying copula approach for constructing a daily financial systemic stress index

This paper develops a financial systemic stress index (FSSI) for the US financial market. We propose a time-varying copula method to model the dependence structure among financial sectors in order to build a correlated financial stress model that can signal systemic financial risks. The copula method is preferable to the traditional approach, enabling the modeling of non-linear correlations. Our analyses show that the dependencies across banking, security, and forex markets are best modeled by Archimedian copulas. Finally, we conduct a Markov Switching Autoregressive (MS-AR) model for FSSI and identify high financial stress episodes taking place in 2008–2009, 2011 and 2020.     

Tests for zero inflation in a bivariate zero‐inflated Poisson model

The score test statistics for testing zero inflation and covariance parameter are proposed in the bivariate zero‐inflated Poisson (BZIP) regression model. The Monte Carlo studies show that the score test and likelihood ratio test for testing zero inflation underestimate the nominal significance level, while the score test for covariance parameter keeps the significance level close to the nominal one. To overcome this nominal level underestimation, we propose a bootstrap method of the score test for the testing problem of zero inflation. An empirical example with covariates is provided to illustrate the results. In addition, score test for zero inflation is also proposed in the BZIP model, which allows a flexible dependence structure using copula.     

An efficient nonparametric estimator for models with nonlinear dependence

We provide a convenient econometric framework for the analysis of nonlinear dependence in financial applications. We introduce models with constrained nonparametric dependence, which specify the conditional distribution or the copula in terms of a one-dimensional functional parameter. Our approach is intermediate between standard parametric specifications (which are in general too restrictive) and the fully unrestricted approach (which suffers from the curse of dimensionality). We introduce a nonparametric estimator defined by minimizing a chi-square distance between the constrained densities in the family and an unconstrained kernel estimator of the density. We derive the nonparametric efficiency bound for linear forms and show that the minimum chi-square estimator is nonparametrically efficient for linear forms.     

Predicting the portfolio risk of high-dimensional international stock indices with dynamic spatial dependence

The spatial dependence of assets, which relates to similarities in economic, political, or cultural systems and other aspects, has been confirmed through empirical research; however, spatial dependence has rarely been applied to financial risk measurement. To fill this gap in the literature, a dynamic spatial GARCH-copula (sGC) model is proposed in this paper to evaluate the portfolio risk of international stock indices. In this model, a spatial GARCH is used as the marginal distribution and vine copula is adopted as the joint distribution of indices. Then, the proposed model is applied empirically to assess portfolio risk. Results show that, first, the proposed risk prediction model with spatial dependence outperforms a model neglecting spatial effects per the Kupiec test, Z test and Christoffersen test. Risk prediction during periods of economic stability is also more accurate than during times of crisis. Second, risk measures for models with spatial dependence are higher than those without such dependence but lower than for vine copula models. Third, models including either spatial dependence or vine copulas alone exhibit relatively poor performance. Fourth, the model involving extreme value theory (EVT) generates the greatest value at risk to pass the Kupiec test, Z test and Christoffersen test; however, this model is not suitable for characterizing international indices with EVT based on negative values of the shape parameters of estimates. Findings offer important implications for personal investors, institutional investors, and national regulatory authorities.     

The adoption of chief diversity officers among S&P 500 firms: Institutional,resource dependence,and upper echelons accounts

The importance of workforce diversity has become a salient management concern given that demographic minorities comprise key sources of the workforce and consumers. As a result, some firms created chief diversity officer (CDO) positions to manage workforce diversity. This study takes a multitheoretic approach, drawing upon institutional, resource dependence, and upper echelons theories to explain firms' adoptions of this key position. Using Cox event history analyses based on a sample of S&P 500 firms, we find that, from an institutional theory perspective, firms are more likely to adopt CDOs when they are headquartered in legalized gay marriage states and the accumulative number of industry CDO adoptions is high. From a resource dependence perspective, we find that firm innovation intensity, diversification levels, transient institutional ownership, and industry female and African American employment bases can predict firms' adoptions of CDO positions. From an upper echelons explanation, we find that female top management team representation is positively associated with firms' adoptions of CDO positions.