heavy-tailed liquidity modeling

This study investigates how to distinguish whether large trades stem from private information or liquidity shocks driven by heavy-tailed distributions, and elucidates the impact of liquidity tail risk on price discovery and market microstructure. To this end, the authors develop a continuous-auction limit order book model under asymmetric information, where market makers observe only aggregate order flow and cannot differentiate informed trades from uninformed liquidity demands following a Student-t distribution. Innovatively treating the heavy-tailed nature of liquidity demand as a key state variable, they characterize equilibrium via a fixed-point equation for marginal cost scheduling and solve it using regular variation asymptotics within a tight class under tail control. The analysis reveals that heavy-tailed liquidity demand attenuates the convexity of price impact, slows the rate of information learning, and induces a regular variation law—governed by the tail index—for the price impact of large orders; notably, fundamental value remains asymptotically revealed even under a constant information arrival rate.

Gaussian models severely underestimate risk when heavy-tailed return distributions coexist with behavioral probability weighting biases. Method: This paper develops an econometric framework that jointly incorporates infinite divisibility and behavioral probability weighting. It innovatively couples a bounded probability weighting function with the Student’s *t* distribution—a heavy-tailed, infinitely divisible distribution—and proposes a joint estimation method for parameter inference. Contribution/Results: The framework simultaneously captures extreme asset return risks (via heavy tails) and nonlinear investor probability distortions (via behavioral weighting). Empirical analysis across 86 assets and over 430,000 daily observations shows that the model significantly outperforms the Gaussian benchmark in 88.4% of samples. At the 99% quantile, Value-at-Risk (VaR) underestimation declines sharply from 19.7% to 3.2%. Moreover, the estimator exhibits strong statistical properties, including consistency and asymptotic normality.

研究通过引入Illiquidity-at-Risk (IlliQaR)指标并考虑跳跃成分，改进了流动性枯竭的预测方法，解决了市场流动性预测问题。

This study addresses the severe inferential bias in conventional predictive ability tests when forecast errors exhibit heavy-tailed distributions—particularly those with infinite variance—where the actual rejection rate at the nominal 5% significance level can surge to as high as 70%. To tackle this issue, the authors establish a new stable limit theorem tailored for strongly mixing time series with infinite variance and propose a subsampling inference method that circumvents the need to estimate either the long-run variance or the tail index, thereby accommodating data with arbitrary tail thickness. The resulting framework delivers robust predictive accuracy testing under heavy-tailedness, substantially correcting the over-rejection problem of traditional tests in emerging market exchange rate risk forecasting and leading to materially revised conclusions about model predictive performance.

Under extreme market events, market efficiency declines, and existing multivariate extreme-value models fail to capture asymmetries in upper- versus lower-tail dependence. Method: This paper proposes the Efficient Tail Hypothesis (ETH), redefining market efficiency through extreme-value theory. It innovatively constructs a regularly varying model defined over the full space ℝᵈ and introduces the Directional Tail Dependence (DTD) measure, establishing the first market efficiency testing framework tailored to extreme behavior—integrating regular variation analysis, multivariate extreme-value statistics, permutation testing, and high-dimensional tail visualization. Contribution/Results: Empirical analysis reveals statistically significant violations of ETH in China’s futures markets, uncovering robust arbitrage opportunities. Concurrently, the study releases a novel high-frequency derivatives dataset, addressing a critical gap in market microstructure research.

This study addresses the challenges of modeling extremes in multivariate high-frequency financial time series—namely, cross-sectional dependence, non-stationarity, and discretization effects—by introducing a novel approach that leverages eigen-decomposition of the correlation matrix. The method projects the original series onto an orthogonal eigenbasis to disentangle market-wide, sector-specific, and idiosyncratic components. Within this decorrelated space, peak-over-threshold (POT) extreme value analysis is applied to each component separately. This work represents the first integration of eigenbasis rotation with extreme value theory in a finite-dimensional dependent system, effectively decoupling collective dynamics from individual noise. By explicitly accounting for non-stationarity and intraday seasonality, the framework enables precise quantification and attribution of tail risk arising from distinct sources.

Traditional normalizing flows struggle to capture the heavy-tailed nature of financial returns, leading to biased estimates of Value-at-Risk (VaR) and Expected Shortfall (ES). This work proposes Lévy-Flow, the first framework to integrate Lévy-driven heavy-tailed distributions—specifically Variance Gamma (VG) and Normal-Inverse Gaussian (NIG)—into normalizing flows. The model explicitly captures tail behavior while preserving exact likelihood computation and enabling efficient reparameterized sampling. Theoretically, it is shown that the proposed flow maintains the tail index under asymptotically linear transformations, which motivates the design of an Identity-tail Neural Spline Flow to faithfully preserve the base distribution’s tail shape. Empirical results on S&P 500 daily returns demonstrate that the VG flow reduces test negative log-likelihood by 69% compared to Gaussian flows and achieves well-calibrated 95% VaR, while the NIG flow yields the most accurate ES estimates.

This study addresses the bias inherent in tail index estimation for heavy-tailed distributions by proposing a novel estimator that integrates bias correction with empirical likelihood. The method uniquely combines bias correction techniques within an empirical likelihood framework to yield a more accurate and stable estimator, accompanied by rigorous asymptotic theory. Simulation experiments demonstrate that the proposed approach significantly outperforms existing methods in finite samples, while empirical analyses on real-world data further confirm its practical effectiveness and applicability.

This study addresses the challenge of measuring systemic risk under extreme market stress by proposing a conditional Value-at-Risk (CoVaR) framework grounded in extreme value theory. By characterizing the limiting behavior of copula-based conditional distributions in joint tail regions, the work establishes, for the first time, an explicit link between CoVaR and the copula’s joint tail structure. It identifies the asymptotic properties of CoVaR under various tail dependence scenarios and develops a unified minimum distance estimation method applicable across diverse tail structures. Empirical analysis demonstrates that the proposed approach effectively uncovers heterogeneous contributions to and exposures from systemic risk across U.S. industries, offering macroprudential regulators and risk managers an interpretable and robust analytical tool.

Traditional Gaussian linear models struggle to capture the nonlinearities and heavy-tailed dependencies in transitioning energy financial markets, which arise from abrupt repricing events, high volatility, and heterogeneous macroeconomic shocks. This study proposes a hybrid forecasting framework that uniquely integrates a Student-t vector autoregression—designed to model multivariate heavy-tailed linear dynamics—with recurrent neural network–based residual learning to extract remaining nonlinear predictability. Out-of-sample rolling forecasts on six representative energy ETFs demonstrate that the proposed approach significantly outperforms conventional VAR models, pure machine learning methods, and other hybrid benchmarks. Notably, predictive gains are most pronounced during periods of market stress, such as the COVID-19 crisis and the Ukraine-related energy shocks, revealing an enhanced nonlinear, heavy-tailed, and regime-sensitive forecasting structure inherent to transitional energy markets under extreme conditions.