arXiv subjects

Chen Tong

Publications and source records attributed to Chen Tong.

15 recordsLinked to original sources

arXiv2026

Split-Session Cluster GARCH for Overnight and Intraday Returns: The Role of Tail Heterogeneity

We propose the Split-Session Cluster GARCH model for heavy-tailed multivariate dependence among asset returns decomposed into overnight and intraday components. The model uses convolution-$t$ distributions to allow tail behavior to differ across clusters defined by trading sessions and, within each session, by economic sectors. It also accommodates block-structured conditional correlation matrices, preserving parsimony and scalability in high-dimensional settings. The resulting likelihood remains tractable and yields a score-driven specification for dynamic correlations. We apply the model to U.S. equity returns in six-asset and 100-asset applications. The results reveal pronounced tail heterogeneity between overnight and intraday returns. Model comparisons show that session-specific tail parameters substantially improve fit relative to a common multivariate-$t$ specification, while sector-level tail partitioning delivers additional gains concentrated mainly in the overnight component. In the 100-asset application, asset-level tail heterogeneity delivers the strongest out-of-sample likelihood and global minimum-variance (GMV) portfolio performance.

econ.EM↗

arXiv2026

Tweedie's Formula and Score-Driven Updating

Score-driven models update time-varying parameters using conditional likelihood scores. This paper develops a Bayesian interpretation of such updates through Tweedie's formula, which connects posterior mean corrections with marginal scores. In Gaussian signal extraction, this gives an exact posterior-correction identity. For natural exponential families, related identities characterize posterior means in natural- and expectation-parameter spaces. Building on these identities, we show that conjugate Bayesian filtering in expectation space coincides exactly with an inverse-Fisher-scaled conditional score update under local precision discounting. For general conditional densities, the exact Bayesian correction involves a generally unavailable predictive-marginal score. A local Gaussian approximation shows that the conditional likelihood score provides the leading approximation to this posterior correction; under local precision discounting, the predictive covariance becomes proportional to inverse Fisher information, yielding the familiar inverse-Fisher-scaled score recursion. The results clarify when score-driven updates are exact Bayesian filters and when they should instead be viewed as tractable local approximations.

econ.EM↗

arXiv2026

Exact Likelihood Inference and Robust Filtering for Gauss-Cauchy Convolution Models

The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, Fisher information, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations. The conditional expectation of the latent Gaussian component is governed by a redescending location score, so extreme observations are automatically discounted rather than propagated. This structure leads to the Gauss-Cauchy Convolution (GCC) filter for state-space models with Gaussian latent dynamics and Voigt measurement errors, where the Masreliez Gaussian prediction approximation preserves a Voigt prediction-error density. In an application to log realized volatility for the Technology Select Sector SPDR Fund, the GCC filter separates persistent latent variation from transient measurement noise and attains the highest implemented prediction-error criterion among the Gaussian, Student-$t$, Huber, and related filtering specifications considered.

econ.EM↗

arXiv2026

The Parabolic Mellin Transform: Gamma and Zeta Integral Representations

We introduce the Parabolic Mellin Transform (PMT), defined by ${P}_{\sigma}[f](z)=\int_{-\infty}^{\infty}w^{2z}f(w^2)dt$, where $w=\sigma+it$ and $\sigma>0$. Under the substitution $u=w^2$, the vertical line $\operatorname{Re}(w)=\sigma$ is mapped to the parabolic contour $C_\sigma$ in the $u$-plane. For the Gaussian kernel, the PMT yields $\int_{-\infty}^{\infty}w^{2z}e^{w^2}dt=\pi/\Gamma(\tfrac{1}{2}-z)=\cos(\pi z)\Gamma(z+\tfrac{1}{2})$, a parabolic-contour form of the classical Hankel representation for the reciprocal Gamma function. The advantage of this parametrization is that the contour integral becomes a Gaussian-damped vertical-line integral. We develop scaling, differentiation, and Dirichlet-composition identities for the PMT and use them to derive integral representations of the Hurwitz zeta, Riemann zeta, and Dirichlet eta functions. The framework provides a unified transform dictionary for Gamma-type and zeta-type special functions and yields equivalent reformulations of the Riemann hypothesis and the Lindel\"of hypothesis in terms of zeros and growth of parabolic-contour integrals.

math.NT↗

arXiv2025

Principled Identification of Structural Dynamic Models

We take a new perspective on identification in structural dynamic models: rather than imposing restrictions alone, we optimize an objective. While definitive structural identification ultimately requires exogenous economic insight, a weighted correlation-maximizing objective yields an Order- and Scale-Invariant Scheme (OASIS) that selects the orthogonal rotation most aligned with designated target variables. In traditional SVARs, these targets are the reduced-form innovations, making OASIS a natural reference rotation. We show that recursive Cholesky identification is a constrained version of the same objective and that OASIS is systematically closer to perfect correlation, closing roughly twice as much of the gap as recursive orderings, both theoretically and empirically. The same framework also provides a principled estimation strategy for Proxy VARs (IV-SVARs), where the weighted criterion is essential for resolving overdetermination in multi-proxy systems while symmetrically accommodating proxy leakage. Revisiting 22 published SVARs, we find that reduced-form innovations are typically only weakly correlated, helping explain the historical robustness of recursive schemes. Applying OASIS to seminal proxy applications, however, reveals economically important leakage across shocks and shows that accounting for such leakage can materially alter substantive conclusions.

econ.EM↗

arXiv2025

Dual-Path Knowledge-Augmented Contrastive Alignment Network for Spatially Resolved Transcriptomics

Spatial Transcriptomics (ST) is a technology that measures gene expression profiles within tissue sections while retaining spatial context. It reveals localized gene expression patterns and tissue heterogeneity, both of which are essential for understanding disease etiology. However, its high cost has driven efforts to predict spatial gene expression from whole slide images. Despite recent advancements, current methods still face significant limitations, such as under-exploitation of high-level biological context, over-reliance on exemplar retrievals, and inadequate alignment of heterogeneous modalities. To address these challenges, we propose DKAN, a novel Dual-path Knowledge-Augmented contrastive alignment Network that predicts spatially resolved gene expression by integrating histopathological images and gene expression profiles through a biologically informed approach. Specifically, we introduce an effective gene semantic representation module that leverages the external gene database to provide additional biological insights, thereby enhancing gene expression prediction. Further, we adopt a unified, one-stage contrastive learning paradigm, seamlessly combining contrastive learning and supervised learning to eliminate reliance on exemplars, complemented with an adaptive weighting mechanism. Additionally, we propose a dual-path contrastive alignment module that employs gene semantic features as dynamic cross-modal coordinators to enable effective heterogeneous feature integration. Through extensive experiments across three public ST datasets, DKAN demonstrates superior performance over state-of-the-art models, establishing a new benchmark for spatial gene expression prediction and offering a powerful tool for advancing biological and clinical research.

q-bio.QM↗

arXiv2025

A Unifying Integral Representation of the Gamma Function and Its Reciprocal

We derive an integral expression $G(z)$ for the reciprocal gamma function, $1/\Gamma(z)=G(z)/\pi$, that is valid for all $z\in\mathbb{C}$, without the need for analytic continuation. The same integral avoids the singularities of the gamma function and satisfies $G(1-z)=\Gamma(z)\sin(\pi z)$ for all $z\in\mathbb{C}$.

math.CV↗

arXiv2025

Dynamic Factor Correlation Model

We introduce a new dynamic factor correlation model with a novel variation-free parametrization of factor loadings. The model is applicable to high dimensions and can accommodate time-varying correlations, heterogeneous heavy-tailed distributions, and dependent idiosyncratic shocks, such as those observed in returns on stocks in the same subindustry. We apply the model to a "small universe" with 12 asset returns and to a "large universe" with 323 asset returns. The former facilitates a comprehensive empirical analysis and comparisons and the latter demonstrates the flexibility and scalability of the model.

econ.EM↗

arXiv2024

Moments by Integrating the Moment-Generating Function

We introduce a general integral framework for computing fractional, complex, absolute, and logarithmic moments from the moment-generating function (MGF) under explicit regularity conditions. By evaluating a complex extension of the MGF along a vertical contour, we obtain exact integral expressions that bypass the need for explicit probability densities and high-order derivatives. We establish conditions for negative fractional moments using the symmetric Cauchy principal value, including the requirement that the distribution have no point mass at the centering point. We demonstrate the theoretical scope and computational practicality of the framework through applications to the normal-inverse Gaussian distribution and a semicontinuous compound Poisson-Gamma distribution. In the latter case, the framework handles point masses at the boundary by evaluating conditional fractional moments.

econ.EM↗

arXiv2024

Cluster GARCH

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution.

econ.EM↗

arXiv2024

Convolution-t Distributions

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody cluster structures with flexible nonlinear dependencies and heterogeneous marginal distributions. Importantly, convolution-t distributions have simple density functions that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are found to be important in an empirical analysis of realized volatility measures and help identify their underlying factor structure.

econ.EM↗

arXiv2023

Characterizing Correlation Matrices that Admit a Clustered Factor Representation

The Clustered Factor (CF) model induces a block structure on the correlation matrix and is commonly used to parameterize correlation matrices. Our results reveal that the CF model imposes superfluous restrictions on the correlation matrix. This can be avoided by a different parametrization, involving the logarithmic transformation of the block correlation matrix.

econ.EM↗

arXiv2022

Option Pricing with State-dependent Pricing Kernel

We introduce a new volatility model for option pricing that combines Markov switching with the Realized GARCH framework. This leads to a novel pricing kernel with a state-dependent variance risk premium and a pricing formula for European options, which is derived with an analytical approximation method. We apply the Markov switching Realized GARCH model to S&P 500 index options from 1990 to 2019 and find that investors' aversion to volatility-specific risk is time-varying. The proposed framework outperforms competing models and reduces (in-sample and out-of-sample) option pricing errors by 15% or more.

q-fin.PR↗

arXiv2022

Option Pricing with Time-Varying Volatility Risk Aversion

We introduce a pricing kernel with time-varying volatility risk aversion to explain observed time variations in the shape of the pricing kernel. When combined with the Heston-Nandi GARCH model, this framework yields a tractable option pricing model in which the variance risk ratio (VRR) emerges as a key variable. We show that the VRR is closely linked to economic fundamentals, as well as sentiment and uncertainty measures. A novel approximation method provides analytical option pricing formulas, and we demonstrate substantial reductions in pricing errors through an empirical application to the S&P 500 index, the CBOE VIX, and option prices.

q-fin.PR↗

arXiv2021

Realized GARCH, CBOE VIX, and the Volatility Risk Premium

We show that the Realized GARCH model yields close-form expression for both the Volatility Index (VIX) and the volatility risk premium (VRP). The Realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with a compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and risk-neutral measures that can explain time-variation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the Realized GARCH model significantly outperforms conventional GARCH models.

econ.EM↗