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28 pages, 789 KB  
Article
Decomposing the Theta Cliff: A SIMDEC Filtering of Asymptotic Time-Decay in Long-Call Options with a Real-Money Intraday Illustration
by George Melville and Julian Yeomans
AI 2026, 7(7), 257; https://doi.org/10.3390/ai7070257 - 12 Jul 2026
Viewed by 593
Abstract
Previous research has shown sector-conditional asymmetry in implied volatility levels and in option returns. However, no prior work has parameterised that asymmetry at the effective-theta layer in a form that fires a non-discretionary rule trigger. This study supplies the parameterisation, its formulation, the [...] Read more.
Previous research has shown sector-conditional asymmetry in implied volatility levels and in option returns. However, no prior work has parameterised that asymmetry at the effective-theta layer in a form that fires a non-discretionary rule trigger. This study supplies the parameterisation, its formulation, the first observation, and the data evidence. An effective theta is defined as Θe=αs,rΘBS, where ΘBS is the standard Black–Scholes (BS) theta and αs,r is a sector- and regime-conditional scaling factor. A SIMDEC decomposition is used to filter the input space and to determine the corner where α matters most. The framework is a bounded retrieval-and-deterministic compute system. The instruments are retrieved from cached market data and the learned layer’s outputs are constrained to that admissible set. Therefore, by construction, it cannot confabulate a fictitious or out-of-bounds instrument and the generative-class hallucination failure mode cannot occur. This concerns the groundedness and bounds of every output and is distinct from the accuracy of the regime and quality labels. SIMDEC supplies the joint-state filtering partition and, together with the Sobol variance decomposition, an explainability and attribution layer in which every position-level evaluation maps to an interpretable joint-state bin and a variance-share attribution. A “first observation” arising from a three-position long-call cohort traversing terminal decay is deployed using eight intraday states tracked on the trajectory at primary-source resolution and illustrates the relationship of the α parameterisation to existing market conditions. To examine the effectiveness of the approach, a SIMDEC dataset from the same deployment supplies population-level support across 12 sectors and a three-tier quality stratification. The dataset is the output of the THETA AI/ML pipeline—a multi-architecture deep-learning inference system that treats SIMDEC joint-state partitioning and Sobol variance decomposition as complementary interpretability inputs, with the regime classifier carrying the labels and the composite quality scorer carrying the stratification. The PC-based, token-free analytical procedure for regulated decision-making settings, together with an illustrative example of the asymmetry in the effective-theta provide a “next level” contribution to traditional option methodology. Full article
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12 pages, 10370 KB  
Article
Transient Potential Profiling for Rapid Calcium Ion Quantification: Eliminating Conditioning Time in Solid-Contact Ion-Selective Electrodes
by Kaijie Zheng, Chenjie Yan, Mengwei Jiang, Jing Lei, Chengcheng Wang, Kai Zhao, Dajing Chen and Min Guo
Biosensors 2026, 16(6), 335; https://doi.org/10.3390/bios16060335 - 12 Jun 2026
Viewed by 595
Abstract
Traditional solid-contact ion-selective electrodes (SC-ISEs) are severely constrained by a long-standing thermodynamic bottleneck, which requires hours of pre-conditioning and stabilization to establish a stable phase-boundary potential. To fundamentally bypass this limitation, we present a paradigm shift in electrochemical ion sensing that exploits dynamic [...] Read more.
Traditional solid-contact ion-selective electrodes (SC-ISEs) are severely constrained by a long-standing thermodynamic bottleneck, which requires hours of pre-conditioning and stabilization to establish a stable phase-boundary potential. To fundamentally bypass this limitation, we present a paradigm shift in electrochemical ion sensing that exploits dynamic kinetics rather than waiting for thermodynamic equilibrium. In this paper, we report a transient potential profiling method that eliminates the need for equilibration by analyzing the open-circuit voltage decay during the first 60 s of polarization. A discharge step on indicator electrode returns the membrane to a reproducible initial state, allowing for the extraction of a concentration correlated coefficient. Using a calcium ISE with an optimized membrane, the early-stage polarization dynamics were fitted to a single exponential saturation model, predicting the steady state response with an average error of 1.6%. The method achieved high repeatability (intra-day RSD 3.22%), batch to batch reproducibility (4.57%), and recovery rates from 90.7% to 115.0% in real water samples. Validation against ion chromatography showed high agreement (R2 = 0.997). This strategy enabled conditioning free, disposable ISEs for point of care and environmental monitoring. Full article
(This article belongs to the Section Nano- and Micro-Technologies in Biosensors)
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39 pages, 5848 KB  
Article
Realized Volatility Forecasting in the Spanish Electricity Market During the 2021–2025 Energy Crisis
by David Veloso-Castello and J. Carlos García-Díaz
Mathematics 2026, 14(12), 2100; https://doi.org/10.3390/math14122100 - 11 Jun 2026
Viewed by 475
Abstract
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 [...] Read more.
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 ROOS2 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 ROOS 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
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29 pages, 2808 KB  
Article
Spatiotemporal Return Decomposition and Multi-Strategy Performance Analysis in Dow Jones Industrial Average Constituents: A 20-Year Empirical Investigation
by Sarthak Pattnaik, Chhayank Jain and Eugene Pinsky
Int. J. Financ. Stud. 2026, 14(6), 145; https://doi.org/10.3390/ijfs14060145 - 3 Jun 2026
Cited by 1 | Viewed by 1609
Abstract
This paper presents a comprehensive spatiotemporal decomposition of equity returns for nine top-weighted constituents of the Dow Jones Industrial Average (DJIA) over a twenty-year period spanning January 2004 through December 2023, encompassing 5033 trading days and multiple market regimes, including the Global Financial [...] Read more.
This paper presents a comprehensive spatiotemporal decomposition of equity returns for nine top-weighted constituents of the Dow Jones Industrial Average (DJIA) over a twenty-year period spanning January 2004 through December 2023, encompassing 5033 trading days and multiple market regimes, including the Global Financial Crisis (2008–2009), the COVID-19 crash and recovery (2020), and the Federal Reserve tightening cycle (2022–2023). Daily price movements are systematically partitioned into two orthogonal sessions: the open-to-close (OTC, or daytime) session, capturing within-session price discovery, and the close-to-open (CTO, or overnight) session, capturing the accumulated information arrival and liquidity dynamics between market closes and subsequent opens. Within this bipartite return framework, we construct and rigorously evaluate 24 distinct trading strategies, spanning directional (long/short), neutral (cash), momentum (inertia), and contrarian (reversal) approaches, applied independently to each session or in combinatorial cross-session configurations. Each strategy is evaluated under three transaction cost regimes (0, 1, and 2 basis points per trade) using an initial investment of $100, and assessed using annualized return, annualised volatility, Sharpe ratio, Sortino ratio, and maximum drawdown. The study universe—comprising UnitedHealth Group (UNH), Goldman Sachs (GS), Microsoft (MSFT), Home Depot (HD), Caterpillar (CAT), Amgen (AMGN), McDonald’s (MCD), Salesforce (CRM), and Honeywell (HON)—captures cross-sector heterogeneity across Healthcare, Financials, Technology, Consumer Discretionary, Industrials, Biotech, and Consumer Staples. The universe is selected from the top-weighted DJIA constituents as of early 2026; the paper is, therefore, best read as a focused, in-depth case study of index-representative large-cap names rather than a general cross-sectional statement about all U.S. equities. The principal findings are threefold. First, the overnight session consistently delivers superior risk-adjusted performance: seven of nine stocks record higher Sharpe ratios during the overnight period versus the daytime period, with the mean overnight Sharpe ratio (0.662) substantially exceeding the mean daytime Sharpe ratio (0.357), a statistically and economically significant overnight premium. Second, the hybrid Strategy #18—Long Overnight coupled with Daytime Reversal—emerges as the dominant cross-asset configuration, generating portfolio values as high as $8464 from a $100 initial investment (AMGN; Sharpe: 0.991) over the 20-year horizon. Third, Trajectory Change Analysis reveals (i) Lévy-stable tails with a mean stability index α¯=1.667 across all constituents, substantially below the Gaussian benchmark of α=2.0; (ii) Hurst exponents clustering below 0.5 (H¯=0.417), confirming dominant mean-reverting dynamics; and (iii) positive rolling CAPM alpha in 51–79% of rolling windows, indicating persistent risk-adjusted outperformance above the S&P 500 benchmark. These findings provide a rigorous empirical foundation for session-aware algorithmic trading system design and challenge the prevailing assumption of temporal homogeneity in equity return processes. Full article
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19 pages, 3417 KB  
Article
Does CNN-Based Feature Extraction Improve High-Frequency Return Prediction? Evidence from the CSI 300 Index
by Fan Zhang and Haobing Wang
J. Risk Financ. Manag. 2026, 19(5), 371; https://doi.org/10.3390/jrfm19050371 - 20 May 2026
Viewed by 551
Abstract
This study investigates whether CNN-based front-end feature extraction improves the predictive performance of deep learning models applied to 1 min intraday CSI 300 index data. Three baseline sequence models, LSTM, GRU, and TCN, are compared against their CNN hybrid and dual-branch fusion variants [...] Read more.
This study investigates whether CNN-based front-end feature extraction improves the predictive performance of deep learning models applied to 1 min intraday CSI 300 index data. Three baseline sequence models, LSTM, GRU, and TCN, are compared against their CNN hybrid and dual-branch fusion variants across five input window sizes, with all comparisons using identical back-end configurations. A total of 45 model configurations are trained and evaluated across 20 independent runs, with performance assessed on four metrics (MAE, RMSE, Directional Accuracy, and Information Coefficient) and statistical significance evaluated by paired t-tests. After standardisation, adding a CNN front-end does not consistently improve performance over the raw baseline and reduces IC for LSTM- and GRU-based models in many cases (e.g., IC of 0.0187 vs. 0.1031 for CNN-LSTM vs. LSTM at W=1), suggesting that standardised recurrent models can extract useful patterns directly from the raw sequence without CNN preprocessing. The dual-branch fusion architecture, which retains both the raw and CNN-compressed sequence branches, consistently outperforms the pure CNN hybrid on MAE, RMSE, and IC for LSTM- and GRU-based models (e.g., LSTMDualBranchFusion achieves statistically significant MAE reductions over CNN-LSTM at W=1, W=2, W=4, and W=5), indicating that the raw sequence carries complementary predictive information that the CNN front-end discards. TCN-based models produce near-zero or negative IC values regardless of architecture variant, suggesting a possible limitation of dilated convolutional architectures for return rank-ordering on this dataset and sample period. These findings are consistent across all five window sizes examined. Full article
(This article belongs to the Special Issue Quantitative Finance in the Era of Big Data and AI)
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26 pages, 1310 KB  
Article
Comparing Daily Volatility Proxies for Cryptocurrency Forecasting Under a Unified Intraday Construction Framework
by Rong-Ho Lin, Rajabali Ghasempour, Amirhossein Nafei, Shu-Chuan Chen and Shu-Lin Chou
Mathematics 2026, 14(10), 1728; https://doi.org/10.3390/math14101728 - 18 May 2026
Viewed by 581
Abstract
This research study compares alternative daily cryptocurrency volatility targets constructed from a common Binance intraday source under a unified and quality-controlled data pipeline. The analysis considers both realized-return-based and range-based measures, including intraday realized variance, calendar-boundary-augmented realized variance, and a realized-range proxy. Forecasting [...] Read more.
This research study compares alternative daily cryptocurrency volatility targets constructed from a common Binance intraday source under a unified and quality-controlled data pipeline. The analysis considers both realized-return-based and range-based measures, including intraday realized variance, calendar-boundary-augmented realized variance, and a realized-range proxy. Forecasting performance is evaluated using direct heterogeneous autoregressive (HAR) models at the 1-, 7-, and 30-day horizons on common out-of-sample support under two complementary loss functions: quasi-likelihood (QLIKE) and log-scale mean squared error. The results show that no universal winner emerges across these criteria. The calendar-boundary-augmented realized variance delivers the best average performance under QLIKE at all horizons, whereas the realized-range proxy performs best under log-scale mean squared error and exhibits greater month-by-month stability. By contrast, classical daily range estimators such as Garman–Klass and Parkinson are not competitive relative to the leading alternatives in this sample. A secondary Bitcoin-conditioned robustness analysis suggests that relative target rankings may vary across market conditions, with stronger contrasts during stress-like episodes. Overall, the findings indicate that the preferred daily volatility target depends primarily on the forecasting objective and should therefore be treated as a substantive empirical choice in cryptocurrency volatility forecasting rather than as a secondary implementation detail. Full article
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31 pages, 380 KB  
Article
A Study on the Performance of Actively and Passively Managed Artificial Intelligence Exchange Traded Funds
by Gerasimos G. Rompotis
J. Risk Financ. Manag. 2026, 19(4), 267; https://doi.org/10.3390/jrfm19040267 - 7 Apr 2026
Viewed by 2956
Abstract
This study employs a sample of 25 active and 22 passive AI ETFs to examine several issues surrounding their performance, risk, pricing efficiency, and persistence in pricing discrepancies and their impact on ETFs’ performance combined with the respective impact of intraday volatility. The [...] Read more.
This study employs a sample of 25 active and 22 passive AI ETFs to examine several issues surrounding their performance, risk, pricing efficiency, and persistence in pricing discrepancies and their impact on ETFs’ performance combined with the respective impact of intraday volatility. The relationship between AI ETFs’ performance and market factors concerning size, value, profitability, investment and momentum is evaluated too. The results indicate that the passive AI ETFs have outperformed active ones over their entire trade history, without, however, shouldering their investors with materially higher volatility. Moreover, both AI ETF groups trade at a persistent premium to their NAV. The concurrent premium positively affects return, while the one-period lagged premium is negatively related to return. In addition, a negative relationship between return and concurrent intraday volatility and a positive (but less strong) relationship between return and one-period lagged intraday volatility are found. Moreover, the majority of AI ETFs do not generate significant alphas. Finally, market factors effectively explain the performance of AI ETFs. Full article
36 pages, 431 KB  
Article
Predicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models
by Abdulrahman Alsamaani and Huda Aldhahi
Int. J. Financ. Stud. 2026, 14(4), 90; https://doi.org/10.3390/ijfs14040090 - 3 Apr 2026
Cited by 1 | Viewed by 3588
Abstract
This study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility [...] Read more.
This study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility (LRE), and heterogeneous autoregressive (HAR) models are systematically compared using 5 min computed return data from September 2018 to September 2020. Our analysis encompasses three forecast horizons (1-day, 7-day, and 30-day) to assess model performance under varying temporal constraints. Through univariate Mincer–Zarnowitz regressions, encompassing tests, and out-of-sample evaluation using root mean squared error (RMSE) and quasi-likelihood loss (QLIKE) functions, we identify significant performance heterogeneity across models and cryptocurrencies. The HAR model exhibits stronger predictive accuracy at short horizons, while EGARCH exhibits relatively stronger performance at longer horizons, although overall explanatory power declines as forecast horizon increases. Importantly, no single model consistently provides optimal forecasts across all cryptocurrencies. Consistent with prior evidence suggesting model performance varies across assets. Encompassing regressions reveal that combining HAR with EGARCH specifications significantly enhances explanatory power across all temporal frames. Out-of-sample Diebold–Mariano tests indicate that HAR generates the lowest forecast errors for most cryptocurrencies, though EGARCH performs exceptionally well for high-market-capitalization assets. These findings provide regime-conditional insights into horizon- and asset-specific volatility dynamics during the pre-institutionalization phase of cryptocurrency markets. The study contributes to emerging literature by incorporating less-dominant cryptocurrencies and offering robust empirical evidence on the asymmetric and persistent volatility characteristics unique to digital asset markets. These findings should be interpreted within the context of the 2018–2020 sample period, representing a pre-institutionalized phase of cryptocurrency markets, and may not fully generalize to structurally different market regimes characterized by increased institutional participation and regulatory development. Full article
34 pages, 2605 KB  
Article
Quasi-Maximum Exponential Likelihood Estimation of Conditional Quantiles for GARCH Models Based on High-Frequency Augmented Data
by Zhenming Zhang, Shishun Zhao, Jianhua Cheng and Anze Wang
Entropy 2026, 28(3), 326; https://doi.org/10.3390/e28030326 - 13 Mar 2026
Viewed by 469
Abstract
GARCH models play a fundamental role in modeling time-varying volatility in financial return series. In practice, financial returns are also well known to exhibit heavy-tailed distributions, which naturally motivates the use of quasi-maximum exponential likelihood estimation (QMELE) for accurately capturing tail behavior and [...] Read more.
GARCH models play a fundamental role in modeling time-varying volatility in financial return series. In practice, financial returns are also well known to exhibit heavy-tailed distributions, which naturally motivates the use of quasi-maximum exponential likelihood estimation (QMELE) for accurately capturing tail behavior and risk measures such as Value-at-Risk. At the same time, the increasing availability of intraday high-frequency data has led to the development of high-frequency augmented GARCH models, which incorporate intraday information into conventional low-frequency volatility frameworks. By exploiting transaction-level data recorded at very fine time scales, these models are able to capture intraday volatility dynamics and market microstructure effects that are not reflected in standard low-frequency observations. Against this background, this paper studies conditional quantile estimation for high-frequency augmented GARCH models. We develop QMELE-based estimators for both model parameters and conditional quantiles, and construct an adjusted test statistic for assessing model adequacy. The asymptotic properties of the proposed estimators and test statistic are established, and their finite-sample performance is examined through extensive simulation studies. Empirical applications to three major stock indices demonstrate that augmenting GARCH models with high-frequency information leads to substantial improvements in conditional quantile estimation compared with traditional low-frequency approaches. Full article
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32 pages, 4314 KB  
Article
A Hardware-Aware Federated Meta-Learning Framework for Intraday Return Prediction Under Data Scarcity and Edge Constraints
by Zhe Wen, Xin Cheng, Ruixin Xue, Jinao Ye, Zhongfeng Wang and Meiqi Wang
Appl. Sci. 2026, 16(5), 2319; https://doi.org/10.3390/app16052319 - 27 Feb 2026
Viewed by 926
Abstract
Although deep learning has achieved remarkable success in time-series prediction, intraday algorithmic trading is characterized by frequent regime shifts (concept drift), which can rapidly render models trained on historical data obsolete in real applications. This motivates on-device adaptation at edge trading terminals. However, [...] Read more.
Although deep learning has achieved remarkable success in time-series prediction, intraday algorithmic trading is characterized by frequent regime shifts (concept drift), which can rapidly render models trained on historical data obsolete in real applications. This motivates on-device adaptation at edge trading terminals. However, practical deployment is constrained by a tripartite bottleneck: real-time samples are scarce, hardware resources on edge are limited, and communication overhead between cloud and edge must be kept low to satisfy stringent latency requirements. To address these challenges, we develop a hardware-aware edge learning framework that combines federated learning (FL) and meta-learning to enable rapid few-shot personalization without exposing local data. Importantly, the framework incorporates our proposed Sleep Node Algorithm (SNA), which turns the “FL + meta-learning” combination into a practical and efficient edge solution. Specifically, SNA dynamically deactivates “inertial” (insensitive) network components during adaptation: it provides a structural regularizer that stabilizes few-shot updates and mitigates overfitting under concept drift, while inducing sparsity that reduces both on-device computation and cloud-edge communication. To efficiently leverage these unstructured zero nodes introduced by SNA, we further design a dedicated accelerator, EPAST (Energy-efficient Pipelined Accelerator for Sparse Training). EPAST adopts a heterogeneous architecture and introduces a dedicated Backward Pipeline (BPIP) dataflow that overlaps backpropagation stages, thereby improving hardware utilization under irregular sparse workloads. Experimental results demonstrate that our system consistently outperforms strong baselines, including DQN, GARCH-XGBoost, and LRU, in terms of Pearson IC. A 55 nm CMOS ASIC implementation further validates robust learning under an extreme 5-shot setting (IC = 0.1176), achieving an end-to-end training speed-up of 11.35× and an energy efficiency of 45.78 TOPS/W. Full article
(This article belongs to the Special Issue Applications of Artificial Intelligence in Industrial Engineering)
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21 pages, 533 KB  
Article
Enhancing Intraday Momentum Prediction: The Role of Volume-Based Information Uncertainty in the Chinese Stock Market
by Decheng Yang and Qiang He
Int. J. Financ. Stud. 2026, 14(2), 47; https://doi.org/10.3390/ijfs14020047 - 14 Feb 2026
Viewed by 5661
Abstract
This study introduces a novel intraday volume-based uncertainty (IVU) proxy—the ratio of opening-half-hour volume to total volume of the preceding seven intervals—to predict final half-hour return direction in the Chinese stock market. Using threshold regression, we identify a statistically significant IVU critical value [...] Read more.
This study introduces a novel intraday volume-based uncertainty (IVU) proxy—the ratio of opening-half-hour volume to total volume of the preceding seven intervals—to predict final half-hour return direction in the Chinese stock market. Using threshold regression, we identify a statistically significant IVU critical value of 0.476225 (p < 0.001), which splits the sample into distinct uncertainty regimes. Logistic regression incorporating this threshold reveals that the joint condition of high opening volume and low IVU (high uncertainty) significantly amplifies the predictive power of initial returns, achieving 63.04% accuracy in the high-uncertainty, high-volume regime. XGBoost further captures complex non-linear interactions, with IVU-related features ranking among the most important predictors and achieving 71.43% out-of-sample accuracy under high-volume, high-uncertainty conditions. A machine learning trading strategy leveraging these predictions yields a total return of 117.99% with a Sharpe ratio of 3.02 over seven years, significantly outperforming benchmarks. Our findings highlight information uncertainty as a critical moderator of intraday momentum and a valuable source of actionable alpha. Full article
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16 pages, 1284 KB  
Article
The Overnight Jump: Disentangling Microstructural and Informational Volatility in TOCOM Rubber Futures
by Chu Chu, Salang Musikasuwan and Rattikan Saelim
J. Risk Financ. Manag. 2025, 18(11), 620; https://doi.org/10.3390/jrfm18110620 - 6 Nov 2025
Cited by 1 | Viewed by 2139
Abstract
The systematic failure of standard Value-at-Risk (VaR) models for the Tokyo Commodity Exchange (TOCOM) rubber futures contract poses significant challenges for risk management. This study addresses the issue by examining the market’s split trading sessions, which induce distinct overnight and intraday volatility regimes. [...] Read more.
The systematic failure of standard Value-at-Risk (VaR) models for the Tokyo Commodity Exchange (TOCOM) rubber futures contract poses significant challenges for risk management. This study addresses the issue by examining the market’s split trading sessions, which induce distinct overnight and intraday volatility regimes. We decompose daily returns into these two components and apply tailored Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family models. Our empirical results, strengthened by extensive robustness checks using EGARCH, IGARCH, and GJR-GARCH specifications, reveal that intraday volatility is persistent and influenced by leverage effects, whereas overnight volatility behaves as a jump-driven process unaccounted for by conventional models. Comprehensive VaR backtesting confirms that while traditional models accurately capture intraday risk, all standard daily models—including asymmetric variants—systematically and severely underestimate overnight risk. These findings demonstrate that aggregating returns into a single daily series conflates different volatility dynamics, leading to model failures. We propose a two-tiered risk management framework that separately applies conventional models to intraday risk and jump-aware measures for overnight risk. This approach aligns risk assessment with underlying market microstructure, improving model validity and capital adequacy for TOCOM rubber futures. Full article
(This article belongs to the Section Financial Markets)
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17 pages, 576 KB  
Article
Using Daily Stock Returns to Estimate the Unconditional and Conditional Variances of Lower-Frequency Stock Returns
by Chris Kirby
Risks 2025, 13(10), 190; https://doi.org/10.3390/risks13100190 - 3 Oct 2025
Cited by 1 | Viewed by 1538
Abstract
If intraday price data are unavailable, then using daily returns to construct realized measures of the variances of lower-frequency returns is a natural substitute for using high-frequency returns in this context. Notably, a suitable application of this approach yields realized measures that are [...] Read more.
If intraday price data are unavailable, then using daily returns to construct realized measures of the variances of lower-frequency returns is a natural substitute for using high-frequency returns in this context. Notably, a suitable application of this approach yields realized measures that are unbiased estimators of the unconditional and conditional variances of holding period returns for any investment horizon. I use a long sample of daily S&P 500 index returns to investigate the merits of constructing realized measures in this fashion. First, I conduct a Monte Carlo study using a data generating process that reproduces the key dynamic properties of index returns. The results of the study suggest that using realized measures constructed from daily returns to estimate the conditional and unconditional variances of lower-frequency returns should lead to substantial increases in efficiency. Next, I fit a multiplicative error model to the realized measures for weekly and monthly index returns to obtain out-of-sample forecasts of their conditional variances. Using the forecasts produced by a generalized autoregressive conditional heteroskedasticity model as a benchmark, I find that the forecasts produced by the multiplicative error model always generate lower mean absolute errors. Furthermore, the improvements in forecasting performance are statistically significant in most cases. Full article
(This article belongs to the Special Issue Volatility Modeling in Financial Market)
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22 pages, 2138 KB  
Article
Stylized Facts of High-Frequency Bitcoin Time Series
by Yaoyue Tang, Karina Arias-Calluari, Morteza Nattagh Najafi, Michael S. Harré and Fernando Alonso-Marroquin
Fractal Fract. 2025, 9(10), 635; https://doi.org/10.3390/fractalfract9100635 - 29 Sep 2025
Viewed by 3940
Abstract
This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transitioning from subdiffusion for short intervals to weak superdiffusion at [...] Read more.
This paper analyzes high-frequency intraday Bitcoin data from 2019 to 2022. The Bitcoin market index exhibits two distinct periods, characterized by abrupt volatility shifts. Bitcoin returns can be described by anomalous diffusion processes, transitioning from subdiffusion for short intervals to weak superdiffusion at longer intervals. Heavy tails are captured well by q-Gaussian distributions, and the autocorrelation of absolute returns shows power law behavior. Both periods display multifractality, with Hurst exponents shifting toward 0.5 over time, indicating increased market efficiency. The time evolution of the empirical PDF of price return allows us to connect these stylized facts to the mathematical framework of multifractals and locally fractional porous medium equations. Full article
(This article belongs to the Special Issue Fractional Porous Medium Type and Related Equations)
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26 pages, 9294 KB  
Article
Bayesian Analysis of Bitcoin Volatility Using Minute-by-Minute Data and Flexible Stochastic Volatility Models
by Makoto Nakakita, Tomoki Toyabe and Teruo Nakatsuma
Mathematics 2025, 13(16), 2691; https://doi.org/10.3390/math13162691 - 21 Aug 2025
Cited by 3 | Viewed by 12054
Abstract
This study analyzes the volatility of Bitcoin using stochastic volatility models fitted to one-minute transaction data for the BTC/USDT pair between 1 April 2023, and 31 March 2024. Bernstein polynomial terms were introduced to accommodate intraday and intraweek seasonality, and flexible return distributions [...] Read more.
This study analyzes the volatility of Bitcoin using stochastic volatility models fitted to one-minute transaction data for the BTC/USDT pair between 1 April 2023, and 31 March 2024. Bernstein polynomial terms were introduced to accommodate intraday and intraweek seasonality, and flexible return distributions were used to capture distributional characteristics. Seven return distributions—normal, Student-t, skew-t, Laplace, asymmetric Laplace (AL), variance gamma, and skew variance gamma—were considered. We further incorporated explanatory variables derived from the trading volume and price changes to assess the effects of order flow. Our results reveal structural market changes, including a clear regime shift around October 2023, when the asymmetric Laplace distribution became the dominant model. Regression coefficients suggest a weakening of the volume–volatility relationship after September and the presence of non-persistent leverage effects. These findings highlight the need for flexible, distribution-aware modeling in 24/7 digital asset markets, with implications for market monitoring, volatility forecasting, and crypto risk management. Full article
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