Stochastic ordering of systemic risk in commodity markets

The contribution of commodity risks to the systemic risk is assessed in this paper through a novel approach that relies on the stochastic property of concordance ordering of CoVaR. Considering the period that spans from 2005 to 2022 and the VIX as the proxy for the stability of the financial system, we build the stochastic ordering of systemic risk for 35 commodities belonging to four sectors: Agriculture, Energy, Industrial Metals, and Precious Metals. The estimates of the ΔCoVaR signal that contagion effects from commodity markets to the financial system have been stronger during the years 2017–2019. Backtests validate CoVaR as a more resilient risk measure than the VaR, especially during periods of market turmoils. The stochastic ordering of CoVaR shows that severe losses (downside risk) in commodity markets tend to exacerbate systemic financial distress more than gains (upside risk). Commodity risks arising from WTI and EUA are threatening triggers for systemic risk. In contrast, the financial system is less vulnerable to a broader range of scenarios arising from fluctuations in Gold prices. As top contributors to the systemic risk, among the sectors we find Energy and Precious Metals with respect to upside risk and downside risk. The Covid-19 crisis has deeply amplified the systemic influence arising from the downside risk of WTI, Gasoline, and Natural Gas UK and has confirmed the safe-haven role of Gold. © 2022 Elsevier B.V.

Stochastic ordering of systemic risk in commodity markets

The contribution of commodity risks to the systemic risk is assessed in this paper through a novel approach that relies on the stochastic property of concordance ordering of CoVaR. Considering the period that spans from 2005 to 2022 and the VIX as the proxy for the stability of the financial system, we build the stochastic ordering of systemic risk for 35 commodities belonging to four sectors: Agriculture, Energy, Industrial Metals, and Precious Metals. The estimates of the ΔCoVaR signal that contagion effects from commodity markets to the financial system have been stronger during the years 2017–2019. Backtests validate CoVaR as a more resilient risk measure than the VaR, especially during periods of market turmoils. The stochastic ordering of CoVaR shows that severe losses (downside risk) in commodity markets tend to exacerbate systemic financial distress more than gains (upside risk). Commodity risks arising from WTI and EUA are threatening triggers for systemic risk. In contrast, the financial system is less vulnerable to a broader range of scenarios arising from fluctuations in Gold prices. As top contributors to the systemic risk, among the sectors we find Energy and Precious Metals with respect to upside risk and downside risk. The Covid-19 crisis has deeply amplified the systemic influence arising from the downside risk of WTI, Gasoline, and Natural Gas UK and has confirmed the safe-haven role of Gold.

Generalization of the Lindley distribution with application to COVID-19 data.

Creating new distributions with more desired and flexible qualities for modeling lifetime data has resulted in a concentrated effort to modify or generalize existing distributions. In this paper, we propose a new distribution called the power exponentiated Lindley (PEL) distribution by generalizing the Lindley distribution using the power exponentiated family of distributions, that can fit lifetime data. Then the main statistical properties such as survival function, hazard function, reverse hazard function, moments, quantile function, stochastic ordering, MRL, order statistics, etc., of the newly proposed distribution have been derived. The parameters of the distribution are estimated using the MLE method. Then, a Monte Carlo simulation study is used to check the consistency of the parameters of the PEL distribution in terms of MSE, RMSE, and bias. Finally, we implement the PEL distribution as a statistical lifetime model for the COVID-19 case fatality ratio (in %) in China and India, and the new cases of COVID-19 reported in Delhi. Then we check whether the new distribution fits the data sets better than existing well-known distributions. Different statistical measures such as the value of the log-likelihood function, K-S statistic, AIC, BIC, HQIC, and p-value are used to assess the accuracy of the model. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.

Jackknife empirical likelihood ratio test for testing mean residual life and mean past life ordering

We propose nonparametric tests for testing mean residual life and mean past life ordering. Asymptotic properties of the proposed test statistics are studied. We also propose Jackknife Empirical Likelihood (JEL) ratio tests for testing mean residual life and mean past life ordering. Some numerical results are presented to evaluate the performance of the proposed tests by comparing them with few competing tests available in the literature. Finally, we illustrate the proposed test procedures using real data sets.