Search Results (95)

Equity-market connectedness can look different depending on whether risk is measured by variance, asymmetry, tail thickness, or jumps. Using 5 min observations for the CSI New Energy Index and ten Shanghai Stock Exchange sector indices from 4 January 2016 to 31 December 2025, we construct 2430 common daily observations of realized volatility, skewness, kurtosis, and jump risk and estimate four TVP-VAR/GFEVD systems. Average total connectedness is 81.2 for volatility, 52.1 for skewness, 41.2 for kurtosis, and 51.1 for jump risk. The new-energy index is a net transmitter in all four full-sample systems, with NET values of 4.7, 4.0, 3.5, and 3.6, respectively, but the dominant transmitter differs by risk dimension: industrials lead volatility and skewness, materials lead kurtosis, and consumer discretionary leads jump risk. Subperiod results show that these roles are not temporally invariant; ZNE becomes a net receiver in several post-2021 risk-measure/period combinations. Alternative lag lengths, forecast horizons, forgetting factors, 15 min aggregation, and an alternative jump-test size leave the broad TVP-VAR conclusions unchanged. The results show that sectoral risk leadership is both dimension-specific and time-varying, with implications for portfolio and sectoral risk monitoring. Full article

Volatility is a core determinant of risk management and return optimization in financial investment. We develop an integrated stock-volatility prediction framework that couples multi-dimensional entropy indicators with machine learning models and links the resulting forecasts to a dynamic Barbell Strategy. The strategy controls drawdowns while retaining upside and remains feasible for individual investors. Using data for the Chinese CSI 300, CSI 500, and CSI 1000 index ETFs and a government bond ETF, we construct predictive features and estimate Yang–Zhang Volatility. The framework incorporates four entropy indicators—Shannon Entropy, Fuzzy Entropy, Permutation Entropy, and Dispersion Entropy—and evaluates model performance under 10-day, 15-day, and 20-day prediction and rebalancing frequencies. The empirical results reveal that the volatility forecasting model for the CSI 1000 has the highest R Squared. In practical trading applications, the Random Forest achieves the optimal risk-adjusted returns, and the 15-day and 20-day portfolio frequencies realize a better trade-off between return and risk control. Full article

Stock market volatility forecasting is important for risk management, portfolio allocation, and investment decision-making. This study provides a bibliometric and methodological review of stock market volatility measurement and forecasting research published between 2016 and 2025. A model-neutral search of the Web of Science Core Collection, conducted on 18 August 2026, identified 440 records. Following title, abstract, full-text, and document-type screening, 177 eligible journal articles were retained. To assess search-term sensitivity, a supplementary search conducted on 4 September 2026 using alternative volatility terminology identified 33 additional eligible studies, yielding a final corpus of 210 studies. Bibliometrix/Biblioshiny and structured methodological classification were used to examine the field. Econometric approaches remained dominant (168 studies; 80.0%), followed by Machine Learning (25; 11.9%), Deep Learning (8; 3.8%), and Hybrid approaches (9; 4.3%). The evidence reveals substantial methodological diversification beyond conventional GARCH models and increasing use of realized and implied volatility, high-frequency information, sentiment, macroeconomic variables, and uncertainty indicators. No methodological family demonstrates universal forecasting superiority, as performance depends on markets, horizons, information sets, benchmarks, and evaluation criteria. Overall, the literature reflects methodological diversification, information enrichment, and selective integration rather than replacement of econometric models by artificial intelligence. Although the review is limited to the Web of Science Core Collection, the sensitivity analysis demonstrates the importance of alternative terminology in identifying relevant studies. Full article

This paper develops a generalized autoregressive conditional heteroskedasticity–mixed data sampling model with continuous and jump components (GARCH-MIDAS-CJ). It aligns the continuous–jump (CJ) decomposition of realized volatility with the long-run–short-run multiplicative structure. The model places block-smoothed daily continuous variation in the long-run mixed-data-sampling term and demeaned jump variation in the short-run Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) recursion. Using high-frequency data for the Standard & Poor’s 500 (S&P 500), we find a positive jump coefficient under both the Corsi–Pirino–Renò (CPR) and Andersen–Bollerslev–Dobrev (ABD) decompositions, supported by one-sided Wald, boundary-adjusted likelihood-ratio, and parametric-bootstrap tests. Relative to return- and realized-measure benchmarks, the forecasting value of the CJ allocation is competitive for multi-day and cumulative variance forecasts and in high-volatility periods, whereas established benchmarks can perform better for one-day and low-volatility forecasts. Under the CPR decomposition, the $h=22$ average cumulative forecasts reduce the mean squared error (MSE) and QLIKE relative to the aggregate-realized-variance benchmark by 8.2% and 3.3%, respectively. One-day-ahead value-at-risk (VaR) results are strongest at the 1% and 0.5% tails; the 5% forecasts have exceedance rates above the nominal level. Across alternative information-timing conventions, forecast windows, and United States equity assets, the clearest gains remain concentrated at multi-day horizons, although their magnitude varies across settings. The findings support a persistence-based allocation of continuous and jump variation within the GARCH-MIDAS structure. Full article

Short-term financial risk in intelligent trading systems is reflected not only in prices, trading volumes, and textual sentiment but also in infrastructure operating states, including server workload, device power consumption, network latency, and packet loss rate. We propose HSF-LLMNet, a hardware sensor and large language model semantic fusion network for jointly modeling external information shocks and infrastructure responses. A large language model extracts event category, sentiment polarity, risk intensity, and semantic uncertainty from financial texts. Reliability-aware temporal modeling handles sensor missingness, drift, and abnormal noise, while asynchronous soft alignment, bidirectional cross-attention, and reliability-aware gated fusion integrate irregular textual events with continuous hardware signals. The model jointly predicts market direction, realized volatility, and three-level risk over the subsequent 30 min. Experiments were conducted on eight Chinese A-share indices: the SSE Composite Index (000001.SH), SSE 50 Index (000016.SH), CSI 300 Index (000300.SH), STAR 50 Index (000688.SH), CSI 500 Index (000905.SH), CSI 1000 Index (000852.SH), Shenzhen Component Index (399001.SZ), and ChiNext Index (399006.SZ). The common observation period for market, textual, and hardware data extended from 1 March 2024 to 30 June 2025. After data cleaning, timestamp matching, and multimodal temporal alignment, 169,208 aligned asset–time prediction windows were retained for the 30 min forecasting task. Realized volatility was defined as the square root of the sum of squared one-minute log returns over the future 30 min interval. The three-level risk label was constructed from future realized volatility, absolute 30 min return, and liquidity stress, with all thresholds estimated exclusively from the training portion of each fold. A sample was labeled high risk when at least two of the three indicators exceeded their 85th-percentile thresholds or when any indicator exceeded its 95th-percentile threshold. It was labeled medium risk when, after excluding high-risk samples, at least two indicators exceeded their 60th-percentile thresholds or any indicator exceeded its 85th-percentile threshold; all remaining samples were labeled low risk. Results showed that HSF-LLMNet achieved an accuracy of 78.62%, a precision of 78.14%, a recall of 77.83%, an F1-score of 77.98%, an area under the receiver operating characteristic curve of 84.91%, and a Matthews correlation coefficient of 57.36% for directional prediction. For realized-volatility regression, the MAE, RMSE, MAPE, and $R^2$ were 0.0089, 0.0135, 9.21%, and 0.812, respectively. For high-risk-event warning, the mean effective warning time, defined as the interval between the first valid alarm and the corresponding event, was 15.37 min; the false-alarm rate and missed-alarm rate were 6.82% and 8.14%, respectively. Ablation experiments showed performance reductions after removing semantic encoding, sensor-reliability estimation, asynchronous alignment, bidirectional cross-attention, gated fusion, or multi-task learning. These results indicate that textual events and infrastructure operating states provide complementary information for quantitative risk analytics and fintech applications. Full article

This paper focuses on China’s gold futures market. Using East Money investor posts and the FinBERT2 model, we construct a multidimensional sentiment indicator comprising overall sentiment, positive/negative intensity, and six fine-grained sentiment categories (happiness, sadness, fear, anger, disgust, and neutral). With high-frequency 5 min data, we compute realized volatility and, within the HAR-RV framework, systematically examine the in-sample and out-of-sample predictive power, asymmetry, and inter-period heterogeneity of sentiment dimensions. The results show that investor sentiment significantly and robustly predicts volatility, with gains increasing over horizons, relying on multi-scale cumulative effects. Predictions are asymmetric: negative sentiment drives volatility while positive sentiment does not. Among fine-grained sentiments, happiness and anger are strongest; fear and sadness are ineffective; and disgust has an effect only in long-term routine forecasts but fails under extreme volatility. During the Russia–Ukraine conflict, sadness replaces happiness and anger as the dominant predictor (long-term MSE: 0.01579 vs. benchmark 0.04384). In trending bull markets, the predictive power of happiness and positive/negative intensity is amplified (full-sample R² gains: 2.70% and 2.89%, vs. 17.08% and 9.69% in bull periods). This study reveals the multidimensional, asymmetric effects and intertemporal heterogeneity of sentiment on forecasts of gold futures volatility, providing a theoretical and empirical foundation for regime-adaptive early-warning systems and risk management. Full article

This study examines whether modern deep learning architectures can improve multi-horizon value-at-risk (VaR) forecasting by learning nonlinear tail-risk dynamics that are difficult to capture with conventional econometric models. Using S&P 500 return data and realized volatility measures, we compare quantile regression (QR), Light Gradient Boosting Machine (LGBM), and five neural architectures—MLP, LSTM, TCN, TiDE, and TFT—within HAR, CAViaR, and realized-volatility-augmented CAViaR specifications across 1% and 5% VaR at 1-day, 5-day, 10-day, and 22-day horizons. Forecast performance is evaluated using pinball loss, formal VaR backtests, and the model confidence set procedure. The results suggest that the performance of deep neural architectures depends on the forecast horizon and the structure of the underlying tail-risk dynamics. In particular, gated memory, attention-based learning, and multi-horizon sequence design appear to improve conditional quantile forecasting by better capturing persistence, nonlinear dependence, and regime-sensitive behavior. At the same time, stronger statistical forecasting accuracy does not automatically imply regulatory validity, since a VaR model must also satisfy formal coverage and independence tests. Overall, the findings highlight the distinction between predictive skill and regulatory adequacy in financial risk measurement. Full article

Wind power producers face severe financial risks from intermittent generation and volatile prices. In this paper, we develop a multivariate scenario-based optimization framework that integrates heavy-tailed Laplace forecast-error path generation, principal component (PC) score matching, and Frequency-Concentrated Projection (FCP) to determine day-ahead bidding curves that maximize expected settlements. To model uncertainty, 24-h scenarios are generated by sequentially accumulating heavy-tailed Laplace forecast-error increments. Trajectories of specific variables are integrated via PC-score matching to construct joint scenarios preserving inter-variable dependencies. A dense optimal response derived from these scenarios is compressed into a market-compatible 11-point bidding curve using FCP, which strategically allocates submission points to highly probable clearing intervals. Evaluation on 2021 NYISO West data demonstrates substantial improvements in both feasibility of scenarios and financial performance. The Laplace specification captures extreme price spikes, so it significantly reduces downside risk compared to a Gaussian baseline. PC-score matching ensures feasibility of structure by preserving daily trajectory shapes. Leveraging these robust scenarios, the FCP curve yields substantially higher realized settlements than the Uniform Support Baseline (USB), which uniformly places the limited submission points across the price range, recovering approximately 90% of the settlement gap between USB and the Dense Optimal Response (DOR), which serves as a non-submittable dense-grid upper-bound benchmark. Ultimately, this framework translates complex uncertainty models into actionable strategies, enabling producers to systematically maximize economic returns under rigid market constraints. Full article

This study analyzes long memory, multifractality and forecasting performance in coffee, Brent oil and gold futures, three international commodity markets of strategic relevance for Colombia. Daily future prices from 2016 to 2025 were examined using logarithmic returns, descriptive statistics, rolling volatility, Hurst R/S, detrended fluctuation analysis (DFA), multifractal detrended fluctuation analysis (MF-DFA), out-of-sample forecasting models, conditional-volatility models and Monte Carlo simulation. The results show heterogeneous long-memory evidence across commodities and market regimes. R/S estimates suggested persistence in the three markets, while DFA moderated this conclusion. MF-DFA confirmed multifractal behavior in all series, with gold and Brent showing wider heterogeneity than coffee. Forecasting results showed that simple models, particularly Random Walk and drift specifications, were difficult to outperform in one-step-ahead predictions. Monte Carlo simulations generated probabilistic price scenarios for 30-, 60- and 90-trading-day horizons, and an ex-post validation with 2026 observed prices showed that six of nine realized prices fell within the simulated P5-P95 intervals. Overall, the findings suggest that commodity futures relevant to Colombia exhibit differentiated forms of temporal complexity, risk and scenario uncertainty that cannot be fully captured by linear models or average volatility measures. Full article

With the rapid expansion of renewable energy and the formal operation of provincial electricity spot markets in China, smart aggregators that coordinate flexible loads, storage resources, demand-response portfolios, and distributed energy resources increasingly face imbalance-settlement risk across the day-ahead and real-time segments of the electricity spot market. Existing studies often focus on average prices or point forecasts, which may overlook regime persistence, negative-price clustering, and tail exposure in high-frequency price spreads. This paper develops a regime-switching and tail-risk signal framework to characterize and forecast day-ahead–real-time price spreads in the Shandong electricity spot market and to translate these forecasts into risk-aware trading signals for representative smart aggregators. Using 35,136 non-public observations at 15 min resolution provided by State Grid Shandong Electric Power Company for 2024, the spread is analyzed using descriptive statistics, Markov regime-switching models, quantile regression, out-of-sample forecasting, trading-signal backtesting, component ablation, and robustness checks. The spread, defined as real-time price minus day-ahead price, has a mean of −7.50 Chinese yuan per megawatt-hour (CNY/MWh), a median of −0.005 CNY/MWh, 5% and 95% quantiles of −196.84 and 137.65 CNY/MWh, and 1% and 99% quantiles of −372.68 and 338.04 CNY/MWh, respectively. A three-state Markov model identifies negative-deviation high-volatility, near-zero low-volatility, and positive-deviation regimes with multi-hour persistence. In the December out-of-sample test, the upper- and lower-tail quantile signals achieve recall rates of 0.872 and 0.841, respectively, and removing lagged spreads increases mean absolute error (MAE) from 24.015 to 54.278 CNY/MWh. The framework provides risk-warning signals rather than causal identification or realized-profit evaluation. Full article

Reliable interval forecasting is essential for risk-aware wind power scheduling, yet the strong nonstationarity and complex spatio-temporal coupling of wind power sequences make probabilistic prediction difficult. This study proposes VSTCformer (Variational-mode-decomposition-enhanced Spatio-Temporal Cross-attention transformer), a wind power interval forecasting framework that integrates adaptive variational mode decomposition (VMD) with spatio-temporal cross-attention and multi-quantile regression. The adaptive VMD module automatically determines the number of modes from the uniformity of center-frequency spacing and decomposes the raw power signal into frequency-aligned intrinsic components, while the undecomposed multivariate sequence is preserved to provide global temporal context. Spatial-guided and temporal-modulated attention realize implicit spatio-temporal coupling during encoding, and explicit fusion is achieved through inter-component interaction before the features are passed to the prediction head. Nine quantiles are jointly estimated to produce the median forecast and prediction intervals at multiple confidence levels. Two public benchmarks with markedly different temporal resolution and volatility are used for evaluation. The results show that VSTCformer preserves competitive point-forecast accuracy while substantially improving interval quality: it produces the narrowest prediction intervals at all evaluated horizons and achieves the best coverage-width trade-off in most settings. The central contribution of the framework is therefore an enhanced and well-calibrated uncertainty quantification capability, confirming that decomposition-enhanced spatio-temporal modeling is an effective route for wind power interval forecasting. Full article

This study proposes a novel hybrid mathematical framework that integrates the Time-Varying Parameter Vector Autoregression (TVP-VAR) connectedness approach with Long Short-Term Memory (LSTM) deep learning networks to analyze, forecast, and manage volatility spillovers in green financial markets. The framework is motivated by the increasing complexity of risk transmission across sustainable assets, including green bonds, renewable energy stocks, carbon markets, and conventional energy assets. The proposed methodology follows a two-stage structure. First, the TVP-VAR model is employed to quantify dynamic connectedness and time-varying spillover effects across markets. Second, the extracted connectedness measures are used as inputs to an LSTM network to forecast future systemic risk dynamics and generate forward-looking variance–covariance matrices for portfolio optimization and hedging purposes. Using daily data from 2015 to 2025, the empirical results reveal that renewable energy stocks are the dominant transmitters of volatility within the system, exerting substantial spillover effects on green bonds and other sustainable assets. The forecasting evaluation demonstrates that the proposed hybrid TVP-VAR-LSTM framework significantly outperforms traditional econometric models (ARIMA and GARCH) as well as conventional machine-learning benchmarks (SVR, Random Forest, and XGBoost), reducing the Root Mean Squared Error (RMSE) by more than 46% in out-of-sample forecasting. Moreover, the enhanced forecasting accuracy translates into economically meaningful benefits, leading to substantial reductions in realized portfolio risk and improved hedging effectiveness. The findings further highlight the importance of carbon pricing mechanisms and standardized green bond certification in mitigating volatility transmission across sustainable financial markets. Overall, this study contributes to the literature on financial mathematics, systemic risk modeling, and machine learning in green finance by providing a unified framework for volatility spillover analysis, forecasting, and dynamic portfolio optimization. Full article

This paper analyzes volatility forecasting in the Spanish electricity spot market over the period 2021–2025, characterized by uncertainty, frequent price jumps, and the increasing occurrence of zero and negative prices. To accommodate these features, electricity prices are shifted to ensure well-defined log-returns, and predictable intraday and seasonal patterns are removed using the Ullrich demeaning procedure. Daily realized volatility measures are constructed from high-frequency data, including jump-robust and noise-robust estimators such as Median Realized Volatility and Realized Kernel. A broad set of volatility models, comprising GARCH-type specifications and multiple extensions of the Heterogeneous Autoregressive (HAR) framework, is evaluated using a coherent out-of-sample forecasting procedure. Model comparison is conducted through the Model Confidence Set methodology based on the QLIKE loss function, which identifies a Superior Set of Models with equal predictive ability. Conditional diagnostics, including Out-of-Sample $R_{\mathrm{OOS}}^2$ measures and Mincer–Zarnowitz regressions, are subsequently used to characterize forecast accuracy, unbiasedness, and efficiency. The empirical results show that all GARCH models are systematically excluded from the superior set, while HAR-type specifications based on realized volatility dominate. Within this set, a HAR model incorporating Median Realized Volatility, jump components, and day-of-the-week effects delivers the strongest economic performance, achieving an Out-of-Sample $R_{\mathrm{OOS} }^2$ close to 0.5 with unbiased forecasts. Overall, the findings highlight the importance of long-memory dynamics, discontinuous price movements, and residual weekly seasonality for volatility forecasting in modern electricity markets. Full article

Next-day S&P 500 direction forecasting matters for allocation, hedging, and risk management because broad-index movements transmit quickly across portfolios. Does structured news sentiment help predict next-day S&P 500 direction? We test four feature sets over 2008–2023 in an ablation sequence: technical indicators only (Set A), with FinBERT headline sentiment (Set B), with BERTopic topic-linked sentiment (Set C), and with realized-volatility weighting (Set D). This design makes two contributions: it separates the incremental value of increasingly structured sentiment features, and it tests whether sentiment value is state-dependent across volatility regimes. CatBoost, XGBoost, LightGBM, LSTM, and GRU are evaluated under walk-forward cross-validation, nested cross-validation, and formal statistical tests. On the full sample, sentiment does not deliver a measurable forecasting edge. Walk-forward AUCs sit near 0.50 for every feature set, and pairwise tests find no significant differences. However, this average masks a consistent pattern. Sentiment becomes more informative during high-volatility periods, suggesting that its value is state-dependent rather than uniform. Rolling AUC swings from 0.28 to 0.71 depending on the market period. When we split by VIX regime, Set D reaches 0.5684 AUC during high-volatility episodes ($n=50$, permutation $p=0.213$) while adding almost nothing in calm markets. Set D also has the lowest fold-to-fold variance and the shallowest drawdown in trading simulations. These results imply that the relevant question is not whether sentiment works in general, but when it does. Sentiment does not help on average; whether it helps during stress is suggestive but unconfirmed and needs more crisis-period data to settle. Full article

Gold mining firms operate in an environment characterized by substantial commodity price volatility, capital intensity, and long investment horizons. Traditional deterministic financial planning frameworks are insufficient to capture the nonlinear and asymmetric risks associated with gold price fluctuations. This study develops a simulation-based scenario planning framework for gold mining firms, integrating deterministic scenario analysis with stochastic price modeling. Using a stylized and benchmark-calibrated financial model intended for methodological illustration rather than firm-specific forecasting, the study evaluates the impact of gold price uncertainty on key financial indicators, including EBITDA, free cash flow, and net present value. Monte Carlo simulations indicate substantial dispersion in financial outcomes, with approximately 28% of simulated realizations producing negative Net Present Value outcomes under baseline assumptions. The results further demonstrate that volatility significantly amplifies downside exposure despite positive expected returns, thereby highlighting the limitations of deterministic planning approaches. The findings suggest that probabilistic scenario-based financial planning provides a more comprehensive framework for evaluating financial resilience and tail-risk exposure in commodity-dependent industries. Full article