Student-t Copula Research Articles

Dynamic dependency between health-care sector and Islamic industry: before, during and after COVID-19 lockdown evidences

Purpose This study aims to empirically explore and compare the dynamic dependency between health-care sector and Islamic industries before, during and after the COVID-19 pandemic. Design/methodology/approach Time-varying student-t copula is used for before, during and after COVID-19 periods. The data used are the daily frequency price series of the selected markets from February 2017 to October 2023. Findings Empirical results found strong evidence of significant impact of the COVID-19 pandemic on the dependence structure of the studied indexes: Co-movements between various sectors are certain. The authors assist also in the birth of new dependence structure with the health-care industry in response to the COVID-19 crisis. This reflects the contagion occurrence from the health-care sector to other sectors. Originality/value By specifically examining the Islamic industry, this study sheds light on the resilience, challenges and opportunities within this sector, contributing novel perspectives to the broader discourse on pandemic-related impacts on economies and industries. Also, this paper conducts a comprehensive temporal analysis, examining the dynamics before, during and after the COVID-19 lockdown. Such approach enables an understanding of how the relationship between the health-care sector and the Islamic industry evolves over time, accounting for both short-term disruptions and long-term effects. By considering the pre-pandemic context, the paper adopts a longitudinal perspective, enabling a deeper understanding of how historical trends, structural factors and institutional frameworks shape the interplay between the health-care sector and the Islamic industry.

An improved agricultural household margin insurance scheme with insured–insurer risk protection: a time-varying copula approach

Agricultural household margin insurance (AHMI) is a crop insurance scheme that considers a farmer's trading capability. The scheme examines farmers' losses in terms of both agricultural input and output using the farmer exchange rate index. In this article, we improve the previous design of the AHMI [A. Ahdika, D. Rosadi, A.R. Effendie, and Gunardi, Household margin insurance of agricultural sector in Indonesia using a farmer exchange rate index, Agric. Finance Rev. 81 (2020), pp. 169–188.] proposed to be implemented in Indonesia – which only provided risk protection for companies – by broadening the formula of losses so that risk protection covers both farmers and companies. We also provide premium payment scenarios, both seasonally and non-seasonally. We employ a time-varying Student-t copula with the extended dynamic parameter to identify the dynamic dependency between the indexes involved in determining the loss variable. We also determine the premium rate for the insurance scheme with various payment scenarios and investigate the implications for farmer survival and company management. Examining the farmer exchange rate index data of Indonesia, the empirical results show that the improved AHMI using a time-varying copula approach produces more reasonable loss estimates and various premium payment options with low premium rates for farmers, compared to either the previous AHMI design or the current crop insurance program in Indonesia.

Uncovered equity parity: new evidence from a copula approach

ABSTRACT This article finds novel evidence on the uncovered equity parity (UEP) condition by employing copula methodology with historical datasets spanning back to 1870. First, across 17 advanced countries over the twentieth century, a higher equity return currency tends to depreciate in real terms at an annual frequency. Moreover, we also find a statistically significant positive tail dependence between the real equity returns differential and the real exchange rate differential. That is, when real currency returns and real equity returns take extreme values, they tend to co-move in the same direction, implying a time-varying UEP condition that is also confirmed by our time-varying Student-t copula estimation. Our novel findings call for richer theoretical explanations on the UEP relationship.

Copula Models of COVID-19 Mortality in Minnesota and Wisconsin

In this study, we assess COVID-19-related mortality in Minnesota and Wisconsin with the aim of demonstrating both the temporal dynamics and the magnitude of the pandemic’s influence from an actuarial risk standpoint. In the initial segment of this paper, we discuss the methodology successfully applied to describe associations in financial and engineering time series. By applying time series analysis, specifically the autoregressive integrated with moving average methods (ARIMA), to weekly mortality figures at the national or state level, we subsequently delve into a marginal distribution examination of ARIMA residuals, addressing any deviation from the standard normality assumption. Thereafter, copulas are utilized to architect joint distribution models across varied geographical domains. The objective of this research is to offer a robust statistical model that utilizes observed mortality datasets from neighboring states and nations to facilitate precise short-term mortality projections. In the subsequent section, our focus shifts to a detailed scrutiny of the statistical interdependencies manifesting between Minnesota and Wisconsin’s weekly COVID-19 mortality figures, adjusted for the time series structure. Leveraging open-source data made available by the CDC and pertinent U.S. state government entities, we apply the ARIMA methodology with subsequent residual distribution modeling. To establish dependence patterns between the states, pair copulas are employed to articulate the relationships between the ARIMA residuals, drawing from fully parametric models. We explore several classes of copulas, comprising both elliptic and Archimedean families. Emphasis is placed on copula model selection. Student t-copula with the marginals modeled by non-standard t-distribution is suggested for ARIMA residuals of Minnesota and Wisconsin COVID mortality as the model of choice based on information criteria and tail cumulation. The copula approach is suggested for the construction of short-term prediction intervals for COVID-19 mortality based on publicly available data.

Return connectedness and volatility dynamics of the cryptocurrency network

The study examines the connectedness of return and volatility spillovers among cryptocurrencies using the Volume Adjusted Return Network Index (VARNI) and the Volume Adjusted Volatility Network Index (VAVNI) developed through the Student-t Copula function and the DCC-MGARCH. The constructed indices, VARNI and VAVNI, identify return contagion and volatility spillover contagion in cryptocurrencies around Coronavirus Disease 2019 (COVID-19) and the recent Russo-Ukrainian War. The results show that VARNI and VAVNI dispersed before the COVID-19 crisis, concentrated during the COVID-19 crisis, and highly concentrated during the Russo-Ukrainian War. Moreover, the Uncertainty Index affects the volatility spillover from one cryptocurrency to another but does not affect the return connectedness.

Dependence Structure between Green Bond Market and Asian Stock Markets: Evidence from India, China and Pakistan

The purpose of the underlying study is to investigate the dependence structure between the selected Asian Stock Market (Pakistan, India, and China) and Green Bonds Market. For this purpose time, a series of daily data of closing prices of all the markets were obtained from 2014 to 2021. Further, the Bivariate copula approach has been used for analyzing the data. The findings of the study reveal that there is a dependence between log-returns of three Asian stock markets (Pakistan, China, and India) and the green bond market as the best fit copula is t-student. The student-t copula work portrays the dependence between arbitrary variables on the two tails. Although this study contributes to the literature by analyzing more countries in the future shall further add to the literature by adding a regional perspective. Lastly, the findings of the study shall aid the investors in portfolio making, risk management, and policymakers as well.

Systematic risk in the biopharmaceutical sector: a multiscale approach

It is well documented that the biopharmaceutical sector has exhibited weak financial returns, contributing to underinvestment. Innovations in the industry carry high risks; however, an analysis of systematic risk and return compared to other asset classes is missing. This paper investigates the time–frequency interconnectedness between stocks in the biotech sector and ten asset classes using daily cross-country data from 1995 to 2019. We capture investors' heterogeneous investment horizons by decomposing time series according to frequencies. Using a maximal overlap discrete wavelet transform (MODWT) and a dynamic conditional correlation (DCC)-Student-t copula, diversification potentials are revealed, helping investors to reap the benefits of investing in biotech. Our findings indicate that the underlying assets exhibit nonlinear asymmetric behavior that strengthens during periods of turmoil.

A dynamic conditional score model for the log correlation matrix

This paper proposes a new model for the dynamics of correlation matrices, where the dynamics are driven by the likelihood score with respect to the matrix logarithm of the correlation matrix. In analogy to the exponential GARCH model for volatility, this transformation ensures that the correlation matrices remain positive definite, even in high dimensions. For the conditional distribution of returns, we assume a student-t copula to explain the dependence structure and univariate student-t for the marginals with potentially different degrees of freedom. The separation into volatility and correlation parts allows for a two-step estimation, which facilitates estimation in high dimensions. We derive estimation theory for one-step and two-step estimation. In an application to a set of six asset indices including financial and alternative assets we show that the model performs well in terms of diagnostics, specification tests, and out-of-sample forecasting.

Multivariate copula procedure for electric vehicle charging event simulation

This paper introduces a novel application area for multivariate copulas in electric vehicle charging event simulation and dependency analysis. We propose a multivariate copula procedure that can be used to generate new synthetic charging events, which retain the complex dependency and correlation structures present in real-world charging events. The paper compares the most popular multivariate copula functions to discover the most reliable one to be used with electric vehicle charging event data. Accurate EV charging event simulation and analysis is crucial in multiple theoretical and practical applications such as charging load and demand response aggregation modelling. Based on multiple goodness-of-fit tests and charging load profiles of simulated charging events, the Student-t copula was found to be the most reliable multivariate copula to be used with EV charging data. Overall, the multivariate copula procedure is effective in analysis and simulation of EV charging events as it retains the inherent variability and complex dependencies of real charging events.

Developing an entropy and copula-based approach for precipitation monitoring network expansion

Extreme precipitation events have been increasing in recent decades and have been causing impacts to human life and property, which requires expansion of existing networks to provide essential information for hydrometeorological analysis. This study developed an entropy and copula-based approach for precipitation monitoring network expansion, aiming at adding stations in ungauged areas with high value of monitoring (VOM), which was estimated through information content and redundancy. The approach was applied to a network in the Taihu Lake basin, China. We grouped the adjacent stations based on Thiessen polygons, computed VOM for each group and identified candidate locations for additional stations. The entropy measures, e.g., joint entropy and total correlation, required to compute VOM were estimated through the principle of maximum entropy (POME) and copula-based joint distribution fitting. We evaluated the performance of five copula families and adopted the Student t-copula as the optimal copula model. Results showed that orographic effect and network density were the main factors that influence VOM variation, i.e., high VOM appeared in the southwest mountain area and the east area with sparsely distributed stations. We also compared the results with those derived from three data quantization methods, among which the rounding technique produced consistent results. The final network schemes were generated by adding stations following a strategy that supports decision preference on the positioning scheme and station number, and were evaluated through the Kriging interpolation error. The proposed approach provides an efficient and a practical way for strengthening a precipitation monitoring system.

Adaptive stochastic risk estimation of firm operating profit

This paper presents an adaptive stochastic approach to model and estimate the risk measures of the operating profit of a non-financial business. On the one hand, exogenous financial market variables specific to a country, including foreign exchange, interest, and inflation rates, are stochastically modeled via ARCH/GARCH, Vasicek, and regime-switching mean-reverting processes, respectively. Then, the dependency among all financial variables is captured via a residual Student-t copula. On the other hand, as opposed to traditional business planning whereby a few discrete base/best/worst-case scenarios are developed through a limited number of fixed models, nine distinct revenue and five non-revenue models, including ARIMA, principal component analysis (PCA), and principal component regression (PCR) are introduced to be adaptively selected to calculate the operating profit of a business. Finally, the stochastic exogenous financial market and operating profit model of the business are integrated to estimate various risk measures, including the CVaR, of the operating profit. The paper concludes with a case study on the adaptive generation of a stochastic business operating model and estimation of risk measures of the operating profit of a sample, publicly-traded corporation.

Empirical comparison of skewed t-copula models for insurance and financial data

Skewed t-copulas recently became popular as a modeling tool of non-linear dependence in statistics. In this paper we consider three different versions of skewed t-copulas introduced by Demarta and McNeill; Smith, Gan and Kohn; and Azzalini and Capitanio. Each of these versions represents a generalization of the symmetric t-copula model, allowing for a different treatment of lower and upper tails. Each of them has certain advantages in mathematical construction, inferential tools and interpretability. Our objective is to apply models based on different types of skewed t-copulas to the same financial and insurance applications. We consider comovements of stock index returns and times-to-failure of related vehicle parts under the warranty period. In both cases the treatment of both lower and upper tails of the joint distributions is of a special importance. Skewed t-copula model performance is compared to the benchmark cases of Gaussian and symmetric Student t-copulas. Instruments of comparison include information criteria, goodness-of-fit and tail dependence. A special attention is paid to methods of estimation of copula parameters. Some technical problems with the implementation of maximum likelihood method and the method of moments suggest the use of Bayesian estimation. We discuss the accuracy and computational efficiency of Bayesian estimation versus MLE. Metropolis-Hastings algorithm with block updates was suggested to deal with the problem of intractability of conditionals.

ANALYSIS OF THE DEPENDENCE STRUCTURE BETWEEN MINERALS PRICES AND THE RAND/USD EXCHANGE RATE USING COPULAS

Copula functions are flexible tools for modelling the dependence structure between variables. In this research, we extend the literature on currency-commodity relationship using copulas. We examine the dependence structure between gold, platinum mineral prices and RAND/USD exchange rate. ARMA (1, 1)-EGARCH (1, 1) and ARMA(1, 1)-APARCH (1, 1) models under different error terms including normal, student-t and skewed student-t were fitted to the returns of commodity prices and the exchange rate. Constants and time varying copulas were then employed to examine the commodity-currency dependence structure. The results show evidence of a positive, strong dependence between gold, platinum prices and the RAND/USD exchange rate. The analysis relies on Clayton, rotated Clayton, Student-t, Gumbel, rotated Gumbel, Plackett and Joe Clayton copulas and provide an indication of leverage effects. The results of the time varying Normal copula indicate that fluctuations in gold and platinum prices generate Rand/USD volatility.

Three Methods to Calculate the Financial Risk Measurement: Value-At-Risk and Expected Shortfall

This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S. stocks, and the reason why these risk factors can be regarded as a market invariant. Then, it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES, and use three methods(the historical estimation method, boudoukh’s mixed method and Monte Carlo method) to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’ risk factors and multivariate student t-copula distribution’s one, finally it figures out that these three calculation results are very close.

Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying

In this study, we analyze the properties of Bitcoin as a diversifier asset and hedge asset against the movement of international market stock indices: S&P500 (US), STOXX50 (EU), NIKKEI (Japan), CSI300 (Shanghai), and HSI (Hong Kong). For this, we use several copula models: Gaussian, Student-t, Clayton, Gumbel, and Frank. The analysis period runs from August 18, 2011 to June 31, 2019. We found that the Gaussian and Student-t copulas are best at fitting the structure dependence between markets. Also, these copulas suggest that under normal market conditions, Bitcoin might act as a hedge asset against the stock price movements of all international markets analyzed. However, the dependence on the Shanghai and Hong Kong markets was somewhat higher. Also, under extreme market conditions, the role of Bitcoin might change from hedge to diversifier. In a time-varying copula analysis, given by the Student-t copula, we found that even under normal market conditions, for some markets, the role of Bitcoin as a hedge asset might fail on a high number of days.

Market Volatility of the Three Most Powerful Military Countries during Their Intervention in the Syrian War

This paper analyzes the volatility dynamics in the financial markets of the (three) most powerful countries from a military perspective, namely, the U.S., Russia, and China, during the period 2015–2018 that corresponds to their intervention in the Syrian war. As far as we know, there is no literature studying this topic during such an important distress period, which has had very serious economic, social, and humanitarian consequences. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH (1, 1)) model yielded the best volatility results for the in-sample period. The weighted historical simulation produced an accurate value at risk (VaR) for a period of one month at the three considered confidence levels. For the out-of-sample period, the Monte Carlo simulation method, based on student t-copula and peaks-over-threshold (POT) extreme value theory (EVT) under the Gaussian kernel and the generalized Pareto (GP) distribution, overstated the risk for the three countries. The comparison of the POT-EVT VaR of the three countries to a portfolio of stock indices pertaining to non-military countries, namely Finland, Sweden, and Ecuador, for the same out-of-sample period, revealed that the intervention in the Syrian war may be one of the pertinent reasons that significantly affected the volatility of the stock markets of the three most powerful military countries. This paper is of great interest for policy makers, central bank leaders, participants involved in these markets, and all practitioners given the economic and financial consequences derived from such dynamics.

Spatial extreme modeling using student t copula approach in Ngawi Regency

Extreme rainfall is an unpredictable phenomenon which causes suffering effect such as flooding. Located on the Equator area, Indonesia results in a high intensity of extreme rainfall. Initial information regarding the patterns, characteristics, and rainfall prediction is needed in order to minimize the negative effect of such phenomenon. A method that can be used to predict extreme rainfall is the spatial extreme value using the copula approach. The copula approach used in this study is student-t copula. The Generalized Extreme Value (GEV) distribution used for the student-t copula with parameter estimation is Pseudo-Maximum Likelihood Estimation (PMLE). The proposed method was applied to model the extreme rainfall atNgawi Regency. An extreme spatial dependency on location is shown by extreme coefficient graphic. The best model that is obtained is based on Akaike Information Criteriation’s (AIC) lowest value. The best model then continues to be used to predict the rainfall intensity return level. The prediction result of the rainfall intensity return level value shows that the maximum value of rainfall intensity increases from year to year in each station.

Defaultable Bond Pricing under the Jump Diffusion Model with Copula Dependence Structure

We study the pricing of a defaultable bond under various dependence structure captured by copulas. For that purpose, we use a bivariate jump-diffusion process to represent a bond issuer’s default intensity and the market short rate of interest. We assume that each jump of both variables occur simultaneously, and that their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process and three copulas, which are a Farlie-Gumbel- Morgenstern copula, a Gaussian copula, and a Student t-copula are used, respectively. We use the joint Laplace transform of the integrated risk processes to obtain the expression of the defaultable bond price with copula-dependent jump sizes. Assuming exponential marginal distributions, we compute the zero coupon defaultable bond prices and their yields using the three copulas to illustrate the bond. We found that the bond price values are the lowest under the Student-t copula, suggesting that a dependence structure under the Student-t copula could be a suitable candidate to depict a riskier environment. Additionally, the hypothetical term structure of interest rates under the risky environment are also upward sloping, albeit with yields greater than 100%, reflecting a higher compensation required by investors to lend funds for a longer period when the financial market is volatile.

Dependence risk analysis in energy, agricultural and precious metals commodities: a pair vine copula approach

ABSTRACT We apply pair vine copulas, specifically the C-vine and R-vine copulas, to examine the conditional multivariate dependence pattern/structure and R-vine copula-based value-at-risk (VaR) to assess financial portfolio risk. We examine the co-dependencies of 13 major commodity markets (which include three energy commodities, six agricultural commodities and four precious metals prices) from 2 January 2003 to 19 December 2016. Dividing our sample into three sub-periods, namely pre-GFC, GFC and post-GFC, we find that the dependencies among commodities undergo changes in a complex manner, changing in different financial conditions, and that the Student-t copula appears on the maximum number of occasions, especially during the GFC period, signifying the existence of fatter tails in the distributions of returns. We further show that the co-dependencies computed using R-vine copulas are best suited to compute the portfolio VaR during the considered time period.

The impact of oil price uncertainty on GCC stock markets

This paper investigates the dynamics of the co-movement of GCC stock market returns with global oil market uncertainty, using an ARMA-DCC-EGARCH and time varying Student-t copula models. Empirical results demonstrate that oil uncertainty has significant and time varying impacts on the GCC stock returns. The GCC stock returns are found to be negatively affected by oil market uncertainty for almost the entire period under examination. More interestingly, we find that the impact of oil price uncertainty differs across GCC member states and allows for grouping. The results also show that the stock markets of Oman and Bahrain are relatively less sensitive to the oil uncertainty factor, thus offering investors and portfolio managers different investment options and portfolio diversification opportunities across GCC members.