Papers

Regime-switching multi-factor models are widely used in quantitative finance, but filtering does not by itself determine when an agent should act on inferred regime changes. We formulate online regime detection with latent factors and hidden regimes as a Bayesian decision problem balancing false alarms, detection delay, and misclassification. Since posterior regime probabilities are generally non-Markovian, the problem is represented as a measure-valued optimal stopping problem and approximated using particle filtering with Monte Carlo dynamic programming. A single-change-point Heston model provides a benchmark. With observed variance, the problem reduces to a two-dimensional Markov free-boundary problem, while under latent variance decisions are based on the filtered posterior measure. Numerical experiments in Heston and regime-switching Vasicek models show that the latent-information procedure can outperform feasible plug-in rules.

Multivariate Hawkes models are widely used to measure endogenous interactions in event data, but latent common signals can generate apparent excitation even without structural interaction. We characterize the resulting linear projection and construct stable, nonnegative Hawkes processes that share the mean intensity and Bartlett spectrum of common-signal models despite having different excitation mechanisms. This establishes a concrete form of second-order non-identification. We derive integrated third-order cumulants for Hawkes processes with Cox immigration and establish generic local identification of normalized structural parameters in two- and three-dimensional systems. An exact-equivalence Monte Carlo experiment demonstrates how third-order information can distinguish mechanisms with identical second-order structure, while revealing substantial finite-sample limitations under weak signals. For a restricted parametric family, we develop Whittle estimation from binned counts, establish consistency and asymptotic normality under appropriate identification conditions, and construct feasible sandwich standard errors accounting for estimated mean intensities. Simulations assess structural recovery and inference accuracy. An application to cryptocurrency transactions illustrates the sensitivity of inferred excitation to model specification and the limitations of structural interpretation based on spectral fit alone.

We propose a structured continuous-time stochastic volatility model for one-day-ahead integrated-variance forecasting. The model introduces a jointly evolving realized-measure state that feeds directly into latent variance dynamics, while correlated Brownian innovations capture return-linked dependence. Parameters are estimated through simulation-based predictive learning, and Monte Carlo simulation forecasts integrated variance. Across 17 equity indices, the proposed model shows strong out-of-sample performance relative to GARCH, GARCH-Itô, Realized GARCH, HAR, and HEAVY benchmarks under QLIKE, MSE, and MAE. Ablation results show that realized-measure feedback provides substantial incremental forecasting value within the proposed framework, while return-linked Brownian dependence contributes more modest complementary gains. The results support incorporating measurement-driven information directly into continuous-time latent volatility dynamics to improve integrated-variance forecasting.

We study whether stock disclosures by recognizable investors generate abnormal market reactions beyond the reactions produced by comparable but non-recognizable managers. We define the Buffett effect as the incremental abnormal return to a disclosed new position that is attributable to the public recognition of the disclosing investor. We construct a recognition index from Wikipedia pageviews and ProQuest news mentions. Using data from 2000 to 2025 we compare market reaction to disclosures of 24 recognizable discretionary funds with disclosures of 24 matched control funds. New-position disclosures by recognizable managers generate a positive disclosure premium over the filing date and the following trading days, and the premium increases with investor recognition. We construct calendar-time portfolios that mechanically copy each group's disclosed purchases and find that copying the most recognized investors earns a significant alpha that persists for months and does not reverse. The evidence is most consistent with an entangled attention-information channel: investor recognition directs scarce investor attention toward selected disclosures, and the information revealed in those disclosures is then capitalized into prices.

We present a statically and dynamically arbitrage-free European option market model with smooth interpolation between option prices, based on the SANOS framework, and prove that its dynamics admit a unique strong solution. In spirit, it is a stochastic model for local volatility when the latter is used as a representation of a European option price surface, not as a pricing model. We illustrate the strength of our approach on S&P Index Option data from January 2022 to August 2025. We show that the model's initial state fits within bid/ask for more than 95% of relevant market option prices. We then train the model dynamics under $\mathbb{P}$ and $\mathbb{Q}$ and show that the model is indeed free of arbitrage while fitting the dynamics of the market well. We also propose a range of BHW-tests to test for absence of arbitrage.

Within the framework of non-extensive statistical mechanics, $q$-Gaussian distributions arise as maximum-entropy solutions of Tsallis entropy under suitable escort moment constraints. Although widely used in physics, biology, geology, finance, and related fields, standard $q$-Gaussians are intrinsically symmetric and cannot capture asymmetric fluctuations often observed in empirical data. We ask whether asymmetry can arise from the Tsallis maximum-entropy principle without externally skewing or joining distributions. We show that this is achieved by retaining the Tsallis entropy and imposing a global escort mean together with distinct downside and upside escort semi-variances. The key step is to reformulate the problem of maximum Tsallis entropy in terms of the escort density. The nonlinear escort constraints then become affine, while maximizing Tsallis entropy becomes equivalent to maximizing a strictly concave functional over a convex feasible set. Consequently, any admissible stationary solution is the unique global maximizer of the corresponding variational problem. The finite-sample approximation properties of the proposed asymmetric $q$-Gaussian are studied through Monte Carlo experiments using synthetic data generated from Azzalini skew-Student distributions. Compared with the classical symmetric $q$-Gaussian, the asymmetric specification systematically provides a closer approximation to synthetic asymmetric heavy-tailed distributions. Finally, we fit the model to return series from major equity indices, a commodity, and cryptocurrencies, and compare its in-sample goodness of fit with that of a symmetric $q$-Gaussian. The results show that the asymmetric model offers a closer in-sample description of unconditional return distributions, most clearly in the tails.

To extend conventional model-level feature importance to economically meaningful portfolio outcomes and decisions, we propose a local first-order attribution-propagation framework that maps allocation-function feature exposures to local sensitivities of sequential portfolio performance metrics. We relate the propagated attributions to Shapley values defined directly for portfolio objectives and derive statistical inference for Sharpe-ratio attributions. The resulting attribution-guided feature-exposure intervention enables post-training adaptation, translating portfolio-metric explanations into out-of-sample decisions without retraining the underlying allocation model. We further introduce temporal stabilisation and cross-model averaging as complementary regularisation mechanisms. Empirically, the interventions yield statistically significant improvements in net Sharpe ratios across different model classes.

Temporal point processes are used both to measure market mechanisms, for example how fast prices absorb news and how much of the reaction is the market responding to itself, and to predict the next event. We show that one algebraic object, the phase-type (Erlang-chain) state space, serves both purposes with exact likelihoods. For measurement, we build a multiscale phase-type Hawkes process whose parameters all enter linearly. Its log-likelihood is concave, and we compute the global maximum together with a Fenchel duality-gap certificate. A Markov embedding gives the response to an exogenous shock, echoes included, in closed form, and this response is stable if and only if the spectral radius of the branching matrix is below one. Applied to six markets around 670 scheduled macroeconomic releases (2022-2026) with a built-in placebo test, the model shows that the direct reaction to CPI, payrolls, PPI and the FOMC statement is absorbed in about a second, while the market's own echoes stretch half of the response to 16-137 s. For prediction, we introduce EPT-X, a neural point process that adds a history-dependent mixture-of-Erlang renewal channel to a linear Hawkes backbone. Its intensity and compensator remain in closed form, its states follow an affine recursion that trains with a parallel scan, and it can start from the certified fit of the measurement model. EPT-X has the best test likelihood on all five LOBSTER order-book streams and on Retweet and Taobao, and is level with the best published model on StackOverflow. We also find that the EasyTPP implementation of IntensityFree clamps short inter-event times before scoring, and that the gaps of the EasyTPP Amazon data are uniform on two fixed intervals.

Feature selection is a central problem in high-dimensional financial regression, where large numbers of engineered variables and strong correlations among predictors reduce model stability and interpretability. $L_1$ regularization (Lasso) is widely used for sparse regression, but its shrinkage can be restrictive when informative signals are spread across correlated variables. Exact sparse regression avoids this shrinkage but requires solving a combinatorial optimization problem that is computationally difficult and is typically fit to minimize in-sample rather than out-of-sample error. This paper presents a feature selection framework based on Monte Carlo Tree Search with Generalized Nested Rollout Policy Adaptation (GNRPA). Feature selection is formulated as a sequential decision process, and candidate subsets are scored by their out-of-sample validation performance rather than training error. The method also supports a lexicographic objective accounting for subset size and multicollinearity. We study this approach on a contemporaneous explanatory regression task: explaining the weekly return of the NASDAQ-100 index from 1,072 engineered features spanning market, macroeconomic, and factor data. This isolates the value of subset selection under multicollinearity from the separate problem of predictive forecasting. On this task, the proposed method identifies sparse feature subsets with higher out-of-sample explanatory power than an optimized Lasso baseline, reaching an out-of-sample $R^2$ of 0.6961 versus 0.6313 for Lasso. These results suggest that Monte Carlo Tree Search is a practical alternative to convex regularization for sparse explanatory feature selection in financial regression, with potential value for factor attribution and risk decomposition where transparency matters as much as out-of-sample fit.

FLEX options are customized exchange-traded contracts allowing participants to choose nonstandard strikes, expirations, exercise styles, and settlement terms while retaining central clearing. We investigate whether single-name FLEX activity leaves measurable footprints in regular listed-option markets and underlying equities. Using a linked dataset of FLEX consolidations, daily open-interest files, listed-option chains, equity returns, and corporate actions over 250 trading days (March 2025-March 2026) across 41 underlyings and 53 event dates, we document three primary empirical findings: (1) Matched-control difference-in-differences estimates reveal a robust post-event increase in listed-option open interest (beta = 0.3061, p = 0.0042, Benjamini-Hochberg p = 0.0168). (2) FLEX activity is strongly selected into high implied-volatility (IV) environments, concentrated in mid-price underlyings (date-fixed-effect ATM IV premium beta = 0.1235, p = 0.0030). (3) Event-day IV-minus-realized-volatility spreads predict execution-stressed short-straddle returns (beta = 0.0366, p = 0.0100). Short-lived equity return effects (CAR_0 difference of -0.85%, p = 0.0442) do not persist over 1-to-5-day horizons. Overall, FLEX activity serves primarily as an observable marker of institutional volatility demand and open-interest positioning rather than a directional stock-return predictor.

We introduce a mean-reverting stochastic differential equation with a three-component stochastic term and show that it generates a hierarchy of steady-state (stationary) distributions. At the top level, the hierarchy is described by a modified-Beta distribution, while one- and two-parameter reductions produce compact-support, power-law-tailed, and exponential-type limiting families within a single stochastic framework. We then construct two generalized extensions of this hierarchy. In the first, the power transformation is applied directly at the level of the stochastic differential equation; in the second, the same transformation is applied only after the stationary modified-Beta hierarchy has been obtained. While these two procedures agree on important lower branches and limiting cases they generally differ at the top level. The generalized hierarchy is therefore not unique: nonlinear transformation and stationary-state reduction do not commute. For both routes, we derive the probability density and cumulative distribution functions, express their parameters in terms of the underlying stochastic dynamics, clarify the relations among their limiting cases, and compare the resulting families with the traditional Generalized Beta framework.

Wavelet-based financial forecasters typically use the transform only to denoise, or reduce it to a single spectral snapshot at the forecast origin, and the convolution that produces the coefficients is usually bilateral, so it can read past the forecast origin. DSTNet instead retains the recent evolution of filter-bank magnitudes as a causal Dynamic Spectral Trajectory, built from seven trailing technical indicators over a twenty-day lookback with a one-sided Morlet-derived filter bank and an explicit burn-in for the left-boundary transient. A factorized Scale-Temporal Spectral Transformer attends along the time and filter-bank axes separately, a learned gate fuses the spectral branch with a CNN-BiLSTM, and horizon-specific gates emit one, three, five, and ten day forecasts in a single pass. We evaluate seven equity indices and gold under a common expanding-window protocol and an untouched one-year hold-out, against nine learned baselines and a random-walk persistence benchmark. Under MAE and MAPE, persistence is the strongest of the ten fixed competitors in 29 of the 32 series-horizon cells and DSTNet is the only model below it in every cell, by 0.7 to 0.9 percent at one day and 3.4 to 4.5 percent at ten days. At one day, paired testing favours DSTNet against the weaker learned baselines but is inconclusive against persistence and the strongest learned forecasters. A downstream allocation diagnostic does not support an equity-timing advantage on any of the seven indices.

Shallow models are special cases of deep models, and deep models theoretically have the potential to outperform the shallow ones. However, the existing empirical asset pricing literature provides strong benchmarks for shallow models. Residual learning allows neural network models in asset pricing to go deeper by preserving and refining their shallow counterparts. The out-of-sample Sharpe ratio for value-weighted long-short portfolios of deep residual models (2.07) is higher than that for the corresponding shallow ones (1.92) and more than twice that of the deep feedforward models (0.89). We show that model depth is a source of additional economic value in asset pricing. Residual learning can be used to deepen other neural-network-based asset pricing models if they contain intermediate layers. Our design also provides one way to scale asset pricing models, making native "large asset pricing models" more feasible.

Market-regime models typically assume a finite set of discrete latent states. We examine whether high frequency limit-order-book dynamics exhibit distinct regime separation or apparent regimes result from discretising an underlying continuum, analysing deep limit-order book data for EURO STOXX 50 index futures across 987 clean trading days from 2022 to 2025 using 30, 45 and 60-second aggregation windows. Market states are represented by symmetric positive definite covariance matrices and analysed under Log-Euclidean and affine-invariant geometries; the resulting state cloud has an effective dimension of approximately 1.4. A causal anomaly layer filters statistical, calendar and rollover contamination, while label-free economic validation evaluates market-state separation independently of volatility-based proxy labels. A 17-method zoo spanning conventional and Riemannian representations, reinforced by full-cloud geometric certificates, consistently favours a continuum over a discrete regime structure. A dominant latent coordinate captures between 83.66% and 85.27% of variation in the covariance-state geometry and tracks VSTOXX without regime labels, remaining stable across years although its average level shifts with market conditions, indicating that conventional regimes are coarse quantisations. A divisive hierarchy spanning macro, macro-subregime, micro and micro-subregime tiers is evaluated using expanding-year walk-forward tests, with out-of-sample performance strongest at the macro tier while finer tiers fail to generalise; continuous fine-scale information nonetheless remains predictive, and its discretisation causes the performance loss. Forecasting performance peaks near ten minutes, reaching a maximum pooled R2_OOS of 0.7483. Overall, the latent stress coordinate defines a stable, low-dimensional geometric continuum that captures market stress and its predictive dynamics.

Learning effective representations helps characterize the structure and dynamics of equity markets from financial data with a low signal-to-noise ratio. Black-box deep models can capture complex patterns but may overfit sample noise and lack explicit economic structure. Meanwhile, classic linear financial models provide interpretable references, but their oversimplified assumptions leave non-linear signals uncaptured. To combine the strengths of these two directions, we propose Stock-JEPA, a joint-embedding predictive framework that learns predictable incremental revisions relative to a point-in-time financial prior. First, we leverage a low-complexity financial model to produce fixed statistics summarizing multi-horizon return and risk. A prior projector then maps these statistics into the target encoder's latent space as an anchor. Second, we design a context-conditioned revision predictor to estimate the future representation's predictable displacement from the anchor. Separate losses update the two branches: the anchor learns from prior statistics, while the revision captures additional predictable information from historical context. Third, we freeze all representation modules and train a downstream readout, evaluating its forecasts through cross-sectional ranking and portfolio performance. Theoretically, we prove that optimal revision reduces the prior anchor's expected squared error for the same future representation by exactly $\mathbb{E}[\|\boldsymbol{\Delta}\|_2^2]$. This non-negative gain is the expected squared magnitude of the additional signal predictable from historical context. Experimentally, Stock-JEPA outperforms 13 strong baselines across large-scale China and U.S. equity universes on 5 key evaluation metrics. Ablation studies and representation analysis further demonstrate the value of the learned revisions for representation learning in equity markets.

We model market impact as the response to submitted order flow net of counterflow from latent traders, activated when price displacements from the level that would prevail without the order exceed individual thresholds. Order flow depletes this pool, and a generalized Langevin equation governs its recovery over several time scales. Its memory kernels are finite sums of exponentials, so its Markovian lift is exact rather than an approximation. For an undepleted pool, aggregation under explicit assumptions on individual trading responses yields an intermediate square-root regime between linear small- and large-order limits, without imposing a square-root impact law. Scaling thresholds and responses with price noise makes impact in this regime proportional to volatility, and thresholds that grow with the execution horizon make it independent of duration. With constant displayed depth, expected round-trip costs are nonnegative under the log-price convention, independently of the memory. Numerical experiments show that depletion narrows the square-root range and that memory spectra producing similar single-order impacts can respond differently after substantial prior trading. Calibration to market data is left to a companion paper.

This paper examines whether a cointegration-based pairs trading strategy between PepsiCo and The Coca-Cola Company is statistically robust and economically exploitable. We first test for cointegration and estimate the spread's mean-reversion dynamics over 2013-2018, then hold these statistical parameters fixed and optimise a threshold-based trading strategy in-sample over 2018-2023. Robustness is assessed through transaction-cost and parameter sensitivity tests, walk-forward validation, and Adjusted and Deflated Sharpe Ratios. The strategy is then evaluated out-of-sample from 2023 to the present, including an analysis of time-varying hedge ratios using rolling OLS and a Kalman filter. The results show that weakening mean-reversion dynamics in the spread undermine the effectiveness of the strategy out-of-sample.

News may reveal systematic risk, but whether its context enhances the construction of systematic risk factors is still unclear. We seek to test whether utilizing a sentence transformer represents an improvement over techniques such as Latent Dirichlet Allocation (LDA) in the coherence of topic term lists generated from unstructured text data. To test this, the same collection of unstructured text data comprising of 394,661 articles and the same downstream financial portfolio construction pipeline were applied with the text layer differing, including the length of article text each model used and how topic terms were ranked: we benchmark LDA against a frozen sentence transformer with k-means clustering. We find that the sentence transformer branch had higher observed scores both in terms of coherence (measured by NPMI) as well as financial performance (measured by Sharpe), although the available tests do not establish outperformance. Further exploratory specifications such as utilizing spherical clustering and multi-horizon exposures had an observed excess-return Sharpe of 1.03 for the combined model. We believe that there is some promise in applying context-aware techniques on unstructured news text, but stricter tests using only information available at each date and broader datasets may be required to enhance the confidence in the observed performance.

Self-evolving agents aim to turn research feedback into reusable skills, tools, and research rules. Whether these accumulated capabilities continue to improve later research requires controlled evaluation. Long-horizon alpha discovery provides a state-dependent setting: once a new factor enters the portfolio, the predictive information already covered changes, so the value of the same candidate or experience may change over time. We introduce EverMine, an empirical framework for studying self-evolving research capabilities in long-horizon alpha discovery. EverMine decomposes the research state into history (Hist), the current factor portfolio (Frontier), and reusable capabilities (Cap). Under matched resource limits, we compare complete runs with fixed or evolving Cap, and replace Cap while holding Hist and Frontier fixed to estimate the conditional value of accumulated capabilities. We also combine full trajectories with historical-state replay to examine how experience-based decisions affect candidate selection and portfolio outcomes. Across 18 long-horizon trajectories, end-to-end comparisons show no consistent gain from Cap evolution. Across 48 continuation branches from shared Hist and Frontier states, accumulated Cap also does not consistently outperform the initial Cap. Parameter tuning of existing factor structures can still improve the portfolio. In an exploratory replay of two screening batches from one Evolving trajectory, some screened-out candidates have positive marginal value at the original state, yet submitting all screened-out candidates sequentially slightly lowers final portfolio IC in both batches. These results show that candidate value depends on the evolving portfolio and submission order, and motivate evaluating self-evolving research capabilities through end-to-end outcomes, conditional capability value, and the consequences of experience-based decisions.

HFT systems are conventionally built as a single-threaded event loop, on the rule that every thread hop adds latency. We test that rule against a measurement study of more than a year of CME market data for the NQ front-month contract, following every packet and matching-engine transaction through the feed's two exchange timestamps, and checking the results against a live production receiver. Packets arrive in near-critical self-exciting clusters that belong to the matching engine's transactions, not to how the exchange packs them. The engine often processes consecutive transactions within a fraction of a microsecond, while the market-data publisher sends at most one packet per publisher period of about 7.5 microseconds, so a burst reaches the receiver as a train of packets one period apart. This yields design principles for HFT systems. First, a receiver that handles each packet within one publisher period never queues on arrivals, however bursty the market; there one thread is best. Second, above that period a queueing tail appears, driven by the timing of transactions, not by packet rate or size, and two threads can be better than one: splitting the servicing chain into two stages on separate threads removes most of the tail at the cost of one hop on the median. Third, only the slowest stage matters, so a split pays only if it shortens it. Fourth, just under the period, where the production receiver runs, the remaining tail comes from multi-message packets and variable service times, and the levers are cost per message and spread of service, not thread count. An analytic framework, a burst-limit throughput identity and an exact reduction of the tandem to a single bottleneck server, supports these results.

Verified income is often unavailable in digital loan applications, forcing lenders to rely on reported income and potentially leading to over-lending, overly conservative offers, or rejection of creditworthy applicants. Cross-institutional data-sharing constraints make this problem especially difficult for smaller lenders with limited training data. We introduce FedIncome, a federated learning framework for income estimation that enables institutions to train a shared model without pooling raw borrower records. Using more than one million LendingClub loans partitioned into $50$ state-level clients, we simulate a heterogeneous lending consortium. The best federated model achieves out-of-time $R^2=0.608$, compared with $0.619$ for a pooled centralised benchmark. Small-sample clients obtain an average out-of-time $R^2$ improvement of $3.8$ percentage points relative to the pooled centralised benchmark, while the fitted client-level relationship places the empirical crossover at approximately $4,790$ training observations in this setting. When pooling is infeasible and the relevant alternative is local-only training, federation improves out-of-time performance across all sample-size groups, with the largest gains for data-scarce clients. We also combine federated income estimates with state- and income-specific debt-to-income thresholds. In a retrospective decision analysis, replacing reported income with the federated estimate increases simulated approval rates with only modest changes in observed default rates. FedIncome supports collaborative learning under data-locality constraints with little aggregate loss relative to pooled training and larger gains relative to local-only estimation.

We develop a model-agnostic framework for noise reduction in high-dimensional time series that explicitly targets optimal recovery of a low-dimensional latent dynamic component contaminated by observational white noise. Under the assumption that the latent dynamics live in a low-dimensional linear dynamic subspace, we characterize the optimal linear projection onto the dynamic subspace and provide a geometric description of the residual error in terms of the relative orientation of the signal and noise spaces. We propose estimators for the dynamic subspace and the optimal projection based on lagged covariance matrices, bootstrap dimension selection, and a low-rank representation of the structured noise. Under mild conditions, the resulting denoised series is shown to converge to its population target at the usual parametric rate. Simulations show that the proposed method can substantially improve subspace estimation, reconstruction error, and one-step-ahead forecast accuracy compared with both orthogonal projection-based denoising and the raw data. The approach is illustrated by empirical applications to high-dimensional stock returns and to a 20-variate time series of macroeconomic indicators.

Language-model agents now run the whole of quantitative factor research: they propose investment factors, backtest them, select the survivors and retire them. We ask which of those jobs an agent should keep. Our answer is governed self-evolution: the agent may propose, and a frozen statistical referee that the agent cannot touch must judge. The referee scores each candidate only on market outcomes revealed after submission, by betting, so its false-discovery guarantee holds at every stopping time for any proposal policy. We cross three proposers (a script, a bandit and a language model) with this referee and with three deliberately leaky ones, in a synthetic world with planted truth, a probe-authoring environment and a ten-year walk-forward on the CSI 500. Who judges sets the number of false admissions: the frozen referee admits 5-11 times fewer sub-threshold factors than the leaky referees under a scripted proposer, and no proposer closes that gap. Who proposes sets the yield: the language model beats the script, matches the bandit, and adds the one capability a bandit lacks, writing its own diagnostic probes. The certificate's price is time: an admitted true factor waits about 500 trading days, and the certified portfolio's Sharpe ratio therefore trails an ungated one. Judging belongs to the procedure; proposing and instrument-making belong to the agent.

Forecasters often score the same units per date against one standardized realized outcome. We show that every standardized forecast splits exactly into a component aligned with this common target and a component uncorrelated with it. Three consequences follow: forecast-error correlation largely mirrors forecast correlation and is therefore a poor measure of diversity; an equally weighted combination beats a no-information forecast only when average alignment is large relative to the combination's dispersion; and the gain from adding a forecaster separates into genuine improvement and mere dilution, which equal-weight admission can mistakenly reward. We develop a cautious selection rule, study it in simulations, and apply it to language-model forecasts of US equity rankings and mechanical signals ranking exchange-traded funds. Selection removes most dilution losses, but no combination beats the no-information forecast.

We examine the conditional volatility dynamics of the USD 1Yx10Y forward swap rate using GARCH(1,1), GJR-GARCH(1,1), and a two-regime Markov-switching GARCH (MSGARCH) model. The analysis uses daily data from 2007 to 2023 and incorporates market-implied measures (ATM swaption volatility and the SRVIX in- dex) together with a broad set of diagnostic tests. Standard GARCH and GJR- GARCH models show stable short-run parameters, but the intercept {\omega} varies markedly across rolling windows, causing instability in the implied long-run vari- ance. This pattern, confirmed by the Nyblom test, motivates adopting a regime- switching specification. MSGARCH mitigates this issue by keeping regime-specific parameters stable and capturing time variation through filtered regime probabili- ties. It delivers the highest log-likelihood and lowest AIC, whereas BIC favours the more parsimonious GJR-GARCH. One-step-ahead backtesting indicates comparable short-horizon accuracy across models, but MSGARCH offers a clearer structural in- terpretation by isolating high- and low-volatility regimes aligned with major market events.

Day-ahead electricity price forecasts support trading and storage decisions, but for battery arbitrage predicting intraday price spreads is more relevant than predicting individual hourly prices. Here we show that a temporal hierarchy forecasting (THieF) framework that jointly reconciles forecasts of hourly electricity prices and all intraday price spreads consistently improves performance across two major European electricity markets and three different forecasting architectures. Using five years of out-of-sample data from Germany and Spain, we obtain accuracy improvements of up to 19.7% and profit gains of up to 10.4% relative to unreconciled hourly price forecasts. The gains persist even for a highly accurate pretrained TabPFN foundation model. Our results demonstrate that exploiting coherent relationships between economically relevant forecasting targets can improve both predictive accuracy and decision value, and that better statistical forecasts do not necessarily imply better economic decisions.

Pairs trading exploits mean reversion in the relationship between related assets. We adapt this idea to political betting markets by modelling the combined implied probability of the two major-party nominees with a latent Ornstein-Uhlenbeck process whose mean-reversion level varies over time and whose observations contain additive noise. Model parameters are estimated from regularly sampled odds data using a state-space likelihood, with consecutive repeated values represented by a single retained observation and the elapsed number of sampling intervals preserved in the continuous-time transition. Parametric-bootstrap upper prediction bounds identify signal times at which the combined implied probability is likely to decline, and a no-intercept Bradley-Terry-type model selects the candidate-specific odds quote. The candidate-selection model is trained on 2020 U.S. presidential-election data and evaluated out of sample on 2024 data. The 2024 analysis produced 130 signals, empirical one-step coverage of 95.1%, a mean synthetic odds-price return of 1.86%, and an unannualized per-trade Sharpe-type ratio of 1.12. These returns are frictionless descriptive quantities rather than executable betting-exchange profits. The results support the integrated framework as a proof of concept for two-candidate electoral markets.

In a statistical factor model, principal components (or eigenvectors) of a sample covariance matrix serve as estimates of principal directions, the true drivers of co-movement of a collection of observed variables. We write the often substantial error in these estimates as a sum of two interpretable terms, which we show have almost sure asymptotic limits as the number of variables grows with sample size bounded. This scenario is commonplace in financial economics, genomics, machine learning and signal processing. Out-of-subspace error measures the distance from an estimate to the subspace spanned by population factor exposures. It can be expressed in terms of data, providing an estimable floor for error. In-subspace error arises from the fixed sample size of the latent factor returns and cannot be estimated from data alone. We illustrate our error analysis with a three-factor simulation of the US public equity market, showing the dependence of the magnitude of the error and its components on dimension and sample size. In that simulation, out-of-subspace error dominates. Researchers who rely on principal component analysis to estimate factor models can use our results to quantify errors in model-based predictions and attributions.

Hybrid Deep Learning for equity index forecasting is limited by three problems: propagation of OHLCV noise into derived technical indicators (TIs), channel-indiscriminate multi-scale decomposition that conflates heterogeneous frequency signatures, and static multi-branch fusion that cannot adapt to market regime shifts. WaVeFuse addresses these limitations through a unified dual-branch architecture. Symlet-4 wavelet denoising (level 2, MAD soft threshold) suppresses microstructure noise in OHLCV. Seven low-lag TIs computed from denoised prices are encoded by a causal channel-wise continuous wavelet transform (Morlet, 32 scales) into a per-timestep scale-space matrix. A CNN-BiLSTM branch captures temporal dynamics, while a dual-layer Transformer (heads=4, dk in {16, 32}) models inter-scale spectral dependencies, and their representations are integrated by a 2-token softmax gate Vertical Attention Fusion (VAF) that dynamically reweights branches as market regimes shift. Evaluated under walk-forward validation (WFV) on KOSPI, DAX, NYSE Composite, and Russell 2000 (2010-2023), WaVeFuse achieves R2 = 0.81-0.96 and directional accuracy 70.5-78.3%. It outperforms seven state-of-the-art models by 8.9-20.2% MAE across twelve dataset-period configurations. Diebold-Mariano statistics (4.62-10.38, p<0.001) confirm superiority over a well-tuned XGBoost benchmark across four indices. Ablation verifies component-wise contributions. Under realistic backtesting with 10 basis point transaction costs, WaVeFuse's directional strategy achieves a mean Sharpe ratio of 3.69 across four markets and limits maximum drawdown to 7.5% during the COVID-19 crash. With 152k parameters (0.68MB) and sub-1.3ms GPU inference, WaVeFuse delivers a computationally efficient, regime-robust framework suitable for research and decision-support deployment.

Special Markowitz (SM) regularises returns and covariance jointly, relative to a reference state (mu_ref, Sigma_ref). Each eigendirection of the whitened relative operator carries a signed spectral potential Phi_k, with persistence factor psi_k = exp(-Phi_k) > 0. Positive potentials attenuate empirical deviations from the reference geometry, zero potential preserves them, and negative potentials amplify them. The persistence factor psi_k governs both the return signal and the covariance deviation: the regularised deviation from the reference is psi_k times the empirical deviation. The logarithmic potential coordinate is characterised by a multiplicative composition law on the multiplicative group of positive real numbers; the Stein loss is characterised as the unique free-energy density (within a natural class) compatible with the resulting coupling. The SM pressure functional is additive across modes the defining property of Special Markowitz.