Energy transition requires huge amounts of critical metals —called energy transition metals (ETMs)— to deploy clean energy technologies. The growing demand for ETMs and uncertainties regarding the ...path to net-zero emissions could cause ETM price oscillations, with potential effects on the prices of other commodities. We explore whether upward and downward movements in ETM prices have a neutral effect on the level and volatility of energy and non-energy commodity prices. By characterizing the conditional dependence between ETM and commodity prices, we document that, except for natural gas, extreme ETM price changes have a non-neutral effect on commodity prices, although this effect vanishes for non-extreme price movements. The implications of this evidence for investors operating in commodity markets are evaluated in terms of commodity risk-adjusted returns, commodity tail risk, and liquidity needs for trading in commodity futures contracts.
•We examine whether ETM price upward and downward movements have a neutral effect on commodity prices.•We characterize conditional dependence between ETM and commodity prices.•Extreme ETM price changes have a non-neutral effect on energy and non-energy commodity prices and volatility.•ETM price movements around median values have negligible effects on commodity prices.•Commodity risk-adjusted returns, tail risk, and liquidity needs can be improved by considering ETM markets.
What elements should a parsimonious model reproduce at a single scale to precisely simulate rainfall at many scales? We posit these elements are: (a) the probability of dry and linear correlation ...structure of the wet/dry sequence as a proxy reproducing the distribution of wet/dry spells, and (b) the marginal distribution of nonzero rainfall and its correlation structure. We build a two‐state rainfall model, the CoSMoS‐2s, that explicitly reproduces these elements and is easily applicable at any timescale. Additionally, the paper: (a) introduces the Generalized Exponential (GE $\mathcal{G}\mathcal{E}$) distribution system comprising six flexible distributions with desired properties to describe nonzero rainfall and facilitate time series generation; (b) extends the CoSMoS framework to allow simulations with negative correlations; (c) simplifies the generation of binary sequences with any correlation structure by analytical approximations; (d) introduces the rank‐based CoSMoS‐2s that preserves Spearman's correlations, has an analytical formulation, and is also applicable for infinite variance time series, (e) introduces the copula‐based CoSMoS‐2s enabling intermittent times series generation with nonzero values having the dependence structure of any desired copula, and (f) offers conceptual generalizations for rainfall modeling and beyond, with specific ideas for future improvements and extensions. The CoSMoS‐2s is tested using four long hourly rainfall records; the simulations reproduce rainfall properties at multiple scales including the wet/dry spells, probability of dry, characteristics of nonzero rainfall, and the behavior of extremes.
Key Points
New flexible system of probability distributions for rainfall intensity
Advanced rainfall generation preserving wet/dry spells, marginal distributions, and copula dependence of nonzero rainfall
Applicable to a single time scale and reproducing rainfall characteristics at multiple scales
Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have ...limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums.
The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining ...given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the European Union. Besides this, the Delegated Regulation by the European Commission requires all insurance companies under supervision to consider different risk scenarios in their risk management system for the company’s own risk assessment. Since it is unreasonable to assume that the potential worst case scenario will materialize in the company, we think that a modelling of various unfavourable scenarios as described in this paper is likewise appropriate. Our explicit copula approach can be considered as a special case of ordinal sums, which in two dimensions even leads to the technically worst VaR scenario.
This paper investigates the dependence structure between the equity market and the foreign exchange market by using copulas. In particular, several copulas with different dependence structure are ...compared and used to directly model the underlying dependence structure. We find that there exists significant symmetric upper and lower tail dependence between the two financial markets, and the dependence remains significant but weaker after the launch of the euro. Our findings have important implications for both global investment risk management and international asset pricing by taking into account joint tail risk.
•The conditional quantiles of several derailment severity outcomes are predicted.•Vine copulas were used to model the underlying complex dependencies within the data.•The model identified tail and ...asymmetric pairwise dependences.•Derailment speed was found to have greatest effect followed by residual train length.•D-vine quantile regression was found to be superior to classical quantile regression.
Although there is a low frequency of train derailments, they have been a major concern due to their high consequences justifying the need to critically examine the severity of train derailments. Derailments may result in injury, loss of life and property, interruption of services and damage of the environment. Most derailment severity models have utilized point estimation approaches which focus on the central tendency of derailment severity outcomes. However, this approach is not reliable given the high variation in derailment severity. Thus, it is imperative to take into consideration the entire severity distribution by examining other statistics including conditional quantiles. Furthermore, derailment data has been found to exhibit tail dependence, skewness and non-normality of the marginal distributions and joint distribution of the variables. Therefore, it is not appropriate to examine their interrelationships using conventional correlation analysis. For these reasons, this paper employs vine copula quantile regression model, an interval estimation approach, to predict conditional mean and quantiles of derailment severity outcomes. This novel methodology automatically tackles prominent issues in classical quantile regression including quantile crossing at various levels and interactions between covariates. Vine copulas, which are multivariate copulas constructed hierarchically from bivariate copulas as building blocks, permit the modeling of the complex dependences between the variables. The vine copula quantile regression model was found to offer better accuracy for analyzing derailment severity at various confidence levels compared to the classical quantile regression approach. The findings provide greater comprehension of the influence of the covariates on train derailment severity.
In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. However, the literature ...mainly focused on the bivariate case, since the constraints on the multivariate copulas correlation matrices would make the specifications of covariates arduous. In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks. We present a novel inferential approach for multivariate distributions, which combines the flexibility of vine constructions with the advantages of Bayesian nonparametrics, not requiring the specification of parametric families for each pair copula. Expressing multivariate copulas using vines allows us to easily account for covariate specifications driving the dependence between response variables. We specify the vine copula density as an infinite mixture of Gaussian copulas, defining a Dirichlet process prior on the mixing measure, and performing posterior inference via Markov chain Monte Carlo sampling. Our approach is successful as for clustering as well as for density estimation. We carry out simulation studies and apply the proposed approach to analyze a veterinary dataset and to investigate the impact of natural disasters on financial development.
Supplementary materials
for this article are available online.
This paper attempts to model both static and dynamic dependence structures and measure impacts of energy consumptions (both renewable (
EC
) and non-renewable (
REN
) energies), economic ...globalization (
GLO
), and economic growth (
GDP
) on carbon dioxide (
CO
2
) emissions in Argentina over the period 1970–2020. For analyses purpose, the current research deploys the novel static and dynamic copula-based ARIMA-fGARCH with different submodels. The static bivariate copula results show that the growth rates of the pairs
EC
-
CO
2
and
GDP
-
CO
2
are asymmetrically positive co-movements and have high left tail (extreme) dependencies, implying that the increase in non-renewable energy and economic growth can critically contribute to the environmental degradation, and the decrease in the consumption of non-renewable energy at a high level will consequently reduce the CO
2
emissions at the same level. Based on several copula-based dependence measures, we document that between the two factors, the non-renewable energy has a stronger impact than the economic growth regarding the CO
2
emissions. On the other hand, the growth rates of both economic globalization and renewable energy symmetrically negatively co-move with the growth rates of the CO
2
emissions, but they have no extreme dependencies, indicating that these factors contribute to Argentina’s environmental quality, in which the factor of renewable energy has a greater impact. Furthermore, the dynamic copula outcomes show that the (tail) dependencies of CO
2
emissions on the non-renewable energy and economic growth are time-varying, while the pairs
REN
-
CO
2
and
GLO
-
CO
2
possess only dynamic dependencies, but no dynamic tail dependencies. Moreover, through the dynamic copula-based dependence, the environmental Kuznets curve (EKC) hypothesis can be estimated and illustrated explicitly. In addition, we leverage multivariate vine copulas for modelling dependence structures of the five variables simultaneously, which can reveal rich information regarding conditional associations among the relevant variables. Some policy implications are also provided to mitigate CO
2
emissions.
Hedging the financial risk of portfolios of securitized real estate assets is daunting because of the unique nature of the underlying assets and because no direct market exists to trade on ...property-related derivatives. In this paper, we conduct a global study of the diversification and risk mitigation benefits of cryptocurrencies for REIT stocks. Specifically, we examine the dynamic relationship between Bitcoin and REIT indices obtained from multiple countries and regions of the world. We also explore whether portfolios of REIT stocks that are hedged with Bitcoin futures obtain significant improvement in portfolio risk mitigation and return performance. Furthermore, given that Bitcoin and REIT stocks are prone to large volatility swings, we examine the nature of the tail dependences in the multivariate distributions of our REIT indices universe and Bitcoin using Archimedean copula functions. Lastly, we compare the market risk of Bitcoin-hedged REIT portfolios to the unhedged portfolios of REIT stocks using value-at-risk. We find region-specific benefits from using Bitcoin to hedge REIT exposure. Furthermore, we show that using Bitcoin to dynamically hedged REIT portfolios had minimal impact on the bivariate and multivariate joint distributions of REIT portfolios. We also find evidence of region-specific reductions in the market risk exposure of dynamically hedged REIT portfolios relative to unhedged and naively hedged REIT portfolios. We posit that Bitcoin could improve the mean-variance frontiers of REIT investors in countries with higher market friction and lower global integration.
•We conduct a global and regional analyses of the benefits of using Bitcoin to enhance the performance of REIT portfolios.•We also examine the nature of the tail dependences in the multivariate distributions of our Bitcoin-enhanced REIT portfolios using Archimedean copula functions.•We compare the market risk of Bitcoin-hedged REIT portfolios to the unhedged portfolios of REIT stocks using value-at-risk.•We find evidence of region-specific benefits from using Bitcoin to hedge REIT exposure.•We also find that using Bitcoin to dynamically hedge REIT portfolios had minimal impact on the tail risk of dynamically hedged REIT portfolios.
Vine copulas provide a way to model a d-dimensional copula with bivariate building blocks and have been applied to a wide range of research topics. The MATVines package is presented, which implements ...vine copula functionalities for MATLAB. In particular, simulation and estimation of regular vine copulas are accommodated. Furthermore, goodness-of-fit testing as well as model comparison tests are provided. The package is exclusively written in MATLAB and uses parallelization for efficient computing where appropriate. As a side effect, it extends the basic copula functionality of MATLAB. The MATVines package is illustrated with several examples.
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