This paper compares the in-sample and out-of-sample performance of several models for computing the tail risk of one-month and one-year electricity futures contracts traded in the NordPool, French, German, and Spanish markets in 2008-2017. As measures of tail risk, we use the one-day-ahead Value-at-Risk (VaR) and the Expected Shortfall (ES). With VaR, the AR (1)-GARCH (1,1) model with Student-t distribution is the best-performing specification with 88% cases in which the Fisher test accepts the model, with a success rate of 94% in the left tail and of 81% in the right tail. The model passes the test of model adequacy in the 100% of the cases in the NordPool and German markets, but only in the 88% and 63% of the cases in the Spanish and French markets. With ES, this model passes the test of model adequacy in 100% of cases in all markets. Historical Simulation and Quantile Regression-based approaches misestimate tail risks. The right-hand tail of the returns is more difficult to model than the left-hand tail and therefore financial regulators and the administrators of futures markets should take these results into account when setting additional regulatory capital requirements and margin account regulations to short positions.
This review presents the set of electricity price models proposed in the literature since the opening of power markets. We focus on price models applied to financial pricing and risk management. We classify these models according to their ability to represent the random behavior of prices and some of their characteristics. In particular, this classification helps users to choose among the most suitable models for their risk management problems.
The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key factor explaining its volatility. During periods of high demand, costlier generation capabilities are utilised since electricity cannot be stored and this has the impact of driving prices up very quickly. Furthermore, the non-storability also complicates physical hedging. Owing to these, the problem of joint price-quantity risk in electricity markets is a com…
Tail risk protection is in the focus of the financial industry and requires solid mathematical and statistical tools, especially when a trading strategy is derived. Recent hype driven by machine learning (ML) mechanisms has raised the necessity to display and understand the functionality of ML tools. In this paper, we present a dynamic tail risk protection strategy that targets a maximum predefined level of risk measured by Value-At-Risk while controlling for participation in bull market regimes. We propose different weak classifiers, parametric and non-parametric, that estimate the exceedance…
In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other fields, when people invest their money in two or more dependent or independent markets, it is very important to know the extreme and total risk before the investment. To find these risk measures for dependent cases is quite challenging, which has not been reported in the literature to the best of our knowledge. We use the FGM copula for modelling the dependenc…
While environmental, social, and governance (ESG) trading activity has been a distinctive feature of financial markets, the debate if ESG scores can also convey information regarding a company's riskiness remains open. Regulatory authorities, such as the European Banking Authority (EBA), have acknowledged that ESG factors can contribute to risk. Therefore, it is important to model such risks and quantify what part of a company's riskiness can be attributed to the ESG scores. This paper aims to question whether ESG scores can be used to provide information on (tail) riskiness. By analyzing the …
We model systemic risk using a common factor that accounts for market-wide shocks and a tail dependence factor that accounts for linkages among extreme stock returns. Specifically, our theoretical model allows for firm-specific impacts of infrequent and extreme events. Using data on the four sectors of the U.S. financial industry from 1996 to 2011, we uncover two key empirical findings. First, disregarding the effect of the tail dependence factor leads to a downward bias in the measurement of systemic risk, especially during weak economic times. Second, when these measures serve as leading ind…
The authors provide a comprehensive overview of flexibility characterization along the dimensions of time, spatiality, resource, and risk in power systems. These dimensions are discussed in relation to flexibility assets, products, and services, as well as new and existing flexibility market designs. The authors argue that flexibility should be evaluated based on the dimensions under discussion. Flexibility products and services can increase the efficiency of power systems and markets if flexibility assets and related services are taken into consideration and used along the time, geography, te…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is unknown, the database is sparse, and therefore special tail models are used. Very often, the generalized Pareto distribution is employed as a basic model, and its parameters are determined with data from the tail area. With the determined tail model, statisticians then calculate the required high quantiles. In this context, we consider the possible accuracy of the …
We present general results on the univariate tail conditional expectation (TCE) and multivariate tail conditional expectation for location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal distributions, location-scale mixture of Student-$t$ distributions, location-scale mixture of Logistic distributions and location-scale mixture of Laplace distributions. We also consider portfolio risk decomposition with TCE for location-scale mixture of elliptical distributions.
When estimating the risk of a financial position with empirical data or Monte Carlo simulations via a tail-dependent law invariant risk measure such as the Conditional Value-at-Risk (CVaR), it is important to ensure the robustness of the statistical estimator particularly when the data contain noise. Kratscher et al. [1] propose a new framework to examine the qualitative robustness of estimators for tail-dependent law invariant risk measures on Orlicz spaces, which is a step further from earlier work for studying the robustness of risk measurement procedures by Cont et al. [2]. In this paper,…
