Search Results (176)

Large-scale hydrogen storage is expected to play a critical role in balancing the variability of renewable energy systems, particularly those driven by wind power. However, the combined influence of storage capacity and deliverability on supply reliability remains insufficiently characterized. This study investigates the reliability limits of hydrogen storage systems operating under variable hydrogen production and time-varying demand. A dimensionless modeling framework is developed to map system performance across a wide range of storage capacities and deliverability levels. The results reveal a clear transition between reliable and unreliable operating regimes. Reliable operation requires a minimum deliverability level approximately equal to the mean hydrogen production rate, corresponding to a value of about 1.05–1.10 times the average production across the range of intermittency conditions considered in this study (from moderate to highly variable production). Below this threshold, increasing storage capacity alone cannot prevent supply shortfalls. Once this threshold is exceeded, further increases in deliverability provide diminishing returns and storage capacity becomes the dominant factor governing reliability. In this regime, the required storage capacity approaches a plateau on the order of 10–30 days of average hydrogen throughput, depending on the level of production variability. The proposed regime-based framework provides a practical tool for evaluating storage feasibility and guiding preliminary capacity design in renewable hydrogen systems. Full article

Following the implementation of Basel IV, China’s financial regulators have replaced Value-at-Risk (VaR) with Expected Shortfall (ES) as the standard market risk measure, necessitating regulatory-oriented evaluation of ES forecasts. This study examines what constitutes a prudent ES forecasting method using e-backtesting, a sequential and model-free evaluation framework designed for regulatory monitoring. We evaluate 11 forecasting methods, including parametric, semiparametric, empirical, and deep-learning models, across four asset classes and four portfolio strategies in the Chinese market under Basel IV-consistent settings. Results show that parametric and semiparametric candidates exhibit clustered backtesting detections and increased computational burden around major market regime shifts, whereas the deep-learning model demonstrates greater resilience and produces more conservative ES forecasts during turbulent periods. These findings suggest that robustness to regime shifts should be considered a key criterion in the regulatory evaluation of ES forecasting models in the Chinese market. Full article

The Hubei carbon emissions trading market presents significant price volatility driven by energy price fluctuations, macroeconomic conditions and policy changes. Accurate price risk measurement is critically important for market participants. This study adopts Value at Risk (VaR) and Expected Shortfall (ES) to quantify market risk, and constructs a set of DCS-type models by combining the dynamic conditional score framework with the skewed Student-t distribution. Model evaluation covers unconditional coverage test, conditional coverage test, dynamic quantile test, the Actual-to-Expected ratio, the mean and the maximum absolute deviation, quantile loss and FZ loss. Empirical analysis based on daily HBEA spot prices from 3 April 2014 to 4 December 2024 shows that: (1) The DCS-ST model provides better data fitting performance and can effectively measure the market risk of China’s carbon trading market. (2) The parameter updating frequency has little impact on the prediction accuracy of the model. The results enriches the quantitative methodology for carbon market risk measurement and provide a reliable technical scheme for tail risk management in China’s carbon emissions trading market. Full article

This paper examines whether climate, geopolitical and economic policy uncertainty indices improve Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts for green and brown stocks. We extend the Realized-ES-CAViaR framework by incorporating physical and transition climate risk, geopolitical risk and economic policy uncertainty indices alongside a high-low range volatility estimator. Using daily data for the iShares Global Clean Energy ETF (ICLN) and the iShares Global Energy ETF (IXC) over the period January 2012–December 2024, we evaluate alternative model specifications at the 1% and 2.5% risk levels through backtesting procedures, strictly consistent scoring rules and the Model Confidence Set methodology. Results reveal a pronounced asymmetry in the predictive content of risk indices across asset classes and quantile levels. Transition climate risk dominates tail-risk forecasting at the 1% level for both asset classes, while geopolitical risk and economic policy uncertainty emerge as the leading factors at the 2.5% level for green and brown stocks, respectively. These findings highlight the heterogeneous channels through which uncertainty shocks propagate into financial tail-risk, with direct implications for risk management and regulatory oversight during the low-carbon transition. Full article

This paper studies an extension of the bilateral gamma process assuming that the drift coefficient may jump at an exponentially distributed random time. The drift switching can reflect the symmetry between major economic events and moves of financial market indexes. The bilateral gamma distribution has an asymmetric form and fits well with different financial data when there are not external shocks. As the main results, we provide exact formulas for the probability density and incomplete moment-generating functions of the stated process. The expressions found are used for risk measurement and European option pricing. The new formulas are determined in particular by values of the incomplete gamma, Whittaker and confluent hypergeometric functions. Numerical examples of the computations are also afforded. The computation time for the formulas is under 4 s in a compiler compatible with MatLab. Full article

We examine whether speculative bubbles in shadow banking institutions contribute to the buildup and materialization of systemic risk. Using the Phillips–Shi–Yu (BSADF) bubble detection methodology and market-based systemic risk measures (ΔCoVaR and Marginal Expected Shortfall), we analyze daily data for 17 publicly listed U.S. shadow banking firms over the period 2010–2026. We document a pronounced pro-cyclical measurement puzzle. During bubble periods, firms exhibit higher market exposure and greater tail risk—Beta increases by 4.9% and Expected Shortfall by 7.9%—yet widely used systemic risk measures decline, with ΔCoVaR falling by 6.6%. This pattern suggests that conventional systemic risk metrics may underestimate vulnerabilities during speculative expansions. However, when bubbles burst, systemic risk materializes rapidly. During burst windows, ΔCoVaR increases by 7.9% and MES by 8.6%, indicating that vulnerabilities accumulated during bubble phases translate into significant systemic spillovers once speculative dynamics collapse. Our findings highlight a pro-cyclical bias in commonly used systemic risk indicators: these measures capture realized financial stress but fail to detect the buildup of fragility during expansion phases. Monitoring bubble dynamics in shadow banking may therefore provide valuable complementary signals for macroprudential surveillance. Full article

This paper compares higher-order co-moment functionals (co-skewness and co-kurtosis) with conditional tail-risk measures, namely Co-Expected Shortfall (CoES) and Co-Value at Risk (CoVaR), within a unified coherence-based framework. On the theoretical side, we present explicit counterexamples showing that co-skewness violates subadditivity and co-kurtosis violates monotonicity, confirming that higher-order co-moments are descriptive diagnostics rather than admissible risk measures. By contrast, CoES inherits the coherence of Expected Shortfall in a conditional joint-tail setting, while CoVaR remains non-coherent and captures tail events only at a quantile level without accounting for loss severity. Empirically, we adopt a predictive, single-index, lagged-conditioning design to examine temporal conditional tail dependence in S&P 500 daily losses from 2007 to 2023. This framework measures the persistence and amplification of market-wide tail risk rather than cross-sectional contagion across institutions. Conditional tail-risk estimates are reported only when the joint tail is sufficiently populated to ensure reliable identification. When these conditions are met, CoES delivers stable and economically interpretable signals of conditional tail fragility, with pronounced elevations during prolonged stress episodes such as the Lehman collapse and the COVID-19 crisis. Robustness analysis at a less extreme tail level confirms that the qualitative ordering of stress regimes is preserved. CoVaR captures sharp conditional stress episodes but exhibits greater sensitivity to sample size, while higher-order co-moments, both raw and standardized, remain sign-unstable and weakly informative. Overall, the results support a clear hierarchy: co-moments as descriptive supplements, CoVaR as a scenario-based stress indicator, and CoES as the coherent benchmark for conditional tail-risk measurement. Full article

This comprehensive review maps how China’s demand-side resources are aggregated, bid into markets, and monetized at the grid edge. We synthesize original studies and pilots to compare edge architectures for local estimation and privacy-preserving coordination, bidding frameworks that span deterministic, stochastic, chance-constrained, and robust designs, and retailer plan optimization that turns wholesale signals into simple user choices. Our headlined findings are fourfold. First, risk-aware bidding frameworks that use chance constraints or conditional value at risk (CVaR) reduce shortfalls without eroding expected revenue when penalties are strict and data are noisy. Second, joint design of retail prices with storage dispatch stabilizes delivery and consumer bills, raising participation and persistence. Third, intraday refresh of envelopes and redispatch improves balance and profit when provincial rules allow updates. Fourth, transparent baselines and settlement rules determine realized value and should be co-designed with aggregation and pricing. We organize reproducible metrics for revenue, reliability, latency, and consumer welfare, and provide simulation templates aligned with Chinese spot practice to enable head-to-head comparisons. The review closes with a research agenda on correlation modeling for heterogeneous portfolios, distribution-aware coordination, and long-run equipment impacts as areas where larger field trials and open data would unlock credible evaluation and faster deployment in China. Full article

Risk management has become increasingly important in the financial world. Considering its importance, it is necessary to measure these risks. The financial market uses two risk measures: Value at Risk (VaR) and Expected Shortfall (ES). After the subprime crisis, the market began to emphasize ES instead of VaR. The hypothesis of this paper to be tested is that longer periods provide better information than shorter, more recent periods for measuring ES volatility to hedge trades. The ES can be adopted using parametric, semi-parametric, and non-parametric methods, and the analyses of the log return indicators started on 3 January 2000 and ended on 5 May 2023. The analyses carried out to evaluate these log return indicators covered the period from 6 May 2023 to 1 August 2025, where it was found that the exchange rate volatility of the Brazilian Real exceeded the VaR limits and even reached the Expected Shortfall risk zone. Then, a different analysis was performed, starting on 11 March 2020 and ending on 5 May 2023. This second analysis, as the first analysis, was carried out to evaluate these log return indicators that covered the period from 6 May 2023 to 1 August 2025. In this latest period analysis, the exchange rate volatility of the Brazilian Real reached the Exchange Shortfall risk zone in a different way compared to the first way. All three types of methods—parametric, non-parametric, and semi-parametric—show distinct behaviors depending on the period evaluated. The hypothesis was rejected, but the hedging strategies should account for asset volatility. The software used to calculate the estimators was Microsoft Excel 365 and Stata 14.2. Full article

This paper examines a stochastic Stackelberg differential game between an insurer and a pool of homogeneous policyholders. Policyholders dynamically optimize insurance coverage and risky asset allocations to minimize the probability of wealth shortfall, while the insurer, acting as the leader, sets the premium loading to maximize the expected exponential utility of terminal surplus. Employing dynamic programming techniques, we derive closed-form equilibrium strategies for both parties. The analysis reveals that a strong positive correlation between insurance claims and financial market returns incentivizes full coverage with modest premiums, whereas a strong negative correlation may induce market collapse as insurers exit underwriting to exploit natural hedging opportunities. Furthermore, larger policyholder pools generate diversification benefits that reduce equilibrium premiums and stimulate insurance demand. Full article

This paper develops a quantitative framework for climate–financial risk measurement that combines a spatially explicit jump–diffusion asset–loss model with prudentially aligned risk metrics. The approach connects regional physical hazards and transition variables derived from climate-consistent pathways to asset returns and credit parameters through the use of climate-adjusted volatilities and jump intensities. Fat tails and geographic heterogeneity are captured by it, which conventional diffusion-based or purely narrative stress tests fail to reflect. The framework delivers portfolio-level Spatial Climate Value-at-Risk (SCVaR) and Expected Shortfall (ES) across scenario–horizon matrices and incorporates an explicit robustness layer (block bootstrap confidence intervals, unconditional/conditional coverage backtests, and structural-stability tests). All ES measures are understood as Conditional Expected Shortfall (CES), i.e., tail expectations evaluated conditional on climate stress scenarios. Applications to bank loan books, pension portfolios, and sovereign exposures show how climate shocks reprice assets, alter default and recovery dynamics, and amplify tail losses in a region- and sector-dependent manner. The resulting, statistically validated outputs are designed to be decision-useful for Internal Capital Adequacy Assessment Process (ICAAP) and Pillar 2: climate-adjusted capital buffers, scenario-based stress calibration, and disclosure bridges that complement alignment metrics such as the Green Asset Ratio (GAR). Overall, the framework operationalises a move from exposure tallies to forward-looking, risk-sensitive, and auditable measures suitable for supervisory dialogue and internal risk appetite. Full article

This research explores the application of extreme value theory in modelling and quantifying tail risks across different economic equity markets, with focus on the Nairobi Securities Exchange (NSE20), the South African Equity Market (FTSE/JSE Top40) and the US Equity Index (S&P500). The study aims to recommend the most suitable probability distribution between the Generalised Extreme Value Distribution (GEVD) and the Generalised Pareto Distribution (GPD) and to assess the associated tail risk using the value-at-risk and expected shortfall. To address volatility clustering, four generalised autoregressive conditional heteroscedasticity (GARCH) models (standard GARCH, exponential GARCH, threshold-GARCH and APARCH (asymmetric power ARCH)) are first applied to returns before implementing the peaks-over-threshold and block maxima methods on standardised residuals. For each equity index, the probability models were ranked based on goodness-of-fit and accuracy using a combination of graphical and numerical methods as well as the comparison of empirical and theoretical risk measures. Beyond its technical contributions, this study has broader implications for building sustainable and resilient financial systems. The results indicate that, for the GEVD, the maxima and minima returns of block size 21 yield the best fit for all indices. For GPD, Hill’s plot is the preferred threshold selection method across all indices due to higher exceedances. A final comparison between GEVD and GPD is conducted to estimate tail risk for each index, and it is observed that GPD consistently outperforms GEVD regardless of market classification. Full article

The Haezendonck–Goovaerts (HG) risk measure defined on Orlicz spaces via the so-called normalised Young function is a direct generalisation of the Expected Shortfall risk measure. The HG measure is known to be a coherent one, thus making it more robust than some of the alternatives, such as Value-at-Risk, for aggregating and comparing risks, and at the same time more flexible for capital allocation problems, risk premium estimation, solvency assessment, and stress testing in insurance and finance. As random risk in practical applications is often assessed in a portfolio setting—a collection of insurance policies or financial assets, like stocks or bonds—we examine the situation in which the total portfolio risk is expressed as the sum of individual random risks. For this, we consider the sum $S_n^{\left(\xi \right)}={\xi }_1+\dots +{\xi }_n$ of possibly dependent and non-identically distributed real-valued random variables ${\xi }_1,\dots ,{\xi }_n$ with consistently varying distributions. Assuming that the collection $\{{\xi }_1,\dots ,{\xi }_n\}$ follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic estimations of the HG risk measure for the sum $S_n^{\left(\xi \right)}$ when the confidence level tends to 1. The formulas presented in our work show that in the case where a portfolio of random losses contains consistently varying losses and the others are asymptotically negligible, it is sufficient for risk assessment to consider only the tails of those dominant losses. Full article

Financial return distributions often exhibit central asymmetry and heavy-tailed extremes, challenging standard parametric models. We propose a novel composite distribution integrating a skew-normal center with skew-t tails, partitioning the support into three regions with smooth junctions. The skew-normal component captures moderate central asymmetry, while the skew-t tails model extreme events with power-law decay, with tail weights determined by continuity constraints and thresholds selected via Hill plots. Monte Carlo simulations show that the composite model achieves superior global fit, lower-tail KS statistics, and stable parameter estimation compared with skew-normal and skew-t benchmarks. We further conduct simulation-based and empirical backtesting of risk measures, including Value-at-Risk (VaR) and Expected Shortfall (ES), using generated datasets and 2083 TSLA daily log returns (2017–2025), demonstrating accurate tail risk capture and reliable risk forecasts. Empirical fitting also yields improved log-likelihood and diagnostic measures (P–P, Q–Q, and negative log P–P plots). Overall, the proposed composite distribution provides a flexible theoretically grounded framework for modeling asymmetric and heavy-tailed financial returns, with practical advantages in risk assessment, extreme event analysis, and financial risk management. Full article

We introduce and study the shortfall of tail-based entropy (STE), a tail-sensitive risk functional that combines expected shortfall (ES) and tail-based entropy (TE). Beyond the tail mean, STE imposes a rank-dependent penalty on tail variability, thereby capturing both the magnitude and variability of tail risk under extremes. The framework encompasses several shortfall-type measures as special cases, such as Gini shortfall, extended Gini shortfall, shortfall of cumulative residual entropy, shortfall of right-tail deviation, and shortfall of cumulative residual Tsallis entropy. We provide equivalent characterizations of STE, derive sufficient conditions for coherence, and establish monotonicity with respect to tail-variability order. As an application, we investigate STE-based capital allocation, deriving closed-form allocation formulas under elliptical and extended skew-normal distributions, along with several illustrative special cases. Finally, an empirical analysis with insurance company data illustrates the implementation and evaluates the performance of the allocation rule. Full article