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<p>Opening price gaps provide an observable measure of how information released outside regular trading hours is incorporated into the first tradable price of the next session. Their empirical distributions often display heavy tails, mild asymmetry, and clustered extreme movements, which are difficult to describe using benchmark distributions based on a single regime structure. This study introduces the <i>t</i>-stable power series (TSPS) distribution as a parametric framework for modelling opening gap rates, referred to as opening diffrates, and overnight tail risk. The model combines a Student-<i>t</i> equilibrium component with a stable power series (SPS) shock component, allowing regular price discovery movements to be separated from random sum information shocks. This structure yields an interpretable decomposition of overnight risk through three quantities: the probability of the shock regime, the tail thickness of individual shock impacts, and the latent frequency of material information arrivals. We apply the framework to opening diffrates of major equity indices, including the Shanghai Composite, S&amp;P 500, DAX, and Nikkei 225, and compare it with Normal, Laplace, Cauchy, Student-<i>t</i>, and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-Stable benchmarks using likelihood-based information criteria and tail diagnostic tools. The empirical results show that the performance of TSPS varies across markets and sample periods. In samples where opening gaps exhibit shock clustering behaviour, the TSPS model provides additional explanatory power and a more informative decomposition of overnight risk. These findings suggest that the TSPS framework is best understood as a diagnostic distributional tool rather than as a uniformly dominant specification. Its practical relevance lies in connecting numerical tail fitting with interpretable risk components that may support overnight VaR and ES assessment, stress testing, and pre-opening risk monitoring.</p>

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Navigating the architecture of overnight jumps: a t-stable power series approach to information shocks and market resilience

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Yuancheng Si,
  • Zili Zhang,
  • Saralees Nadarajah

摘要

Opening price gaps provide an observable measure of how information released outside regular trading hours is incorporated into the first tradable price of the next session. Their empirical distributions often display heavy tails, mild asymmetry, and clustered extreme movements, which are difficult to describe using benchmark distributions based on a single regime structure. This study introduces the t-stable power series (TSPS) distribution as a parametric framework for modelling opening gap rates, referred to as opening diffrates, and overnight tail risk. The model combines a Student-t equilibrium component with a stable power series (SPS) shock component, allowing regular price discovery movements to be separated from random sum information shocks. This structure yields an interpretable decomposition of overnight risk through three quantities: the probability of the shock regime, the tail thickness of individual shock impacts, and the latent frequency of material information arrivals. We apply the framework to opening diffrates of major equity indices, including the Shanghai Composite, S&P 500, DAX, and Nikkei 225, and compare it with Normal, Laplace, Cauchy, Student-t, and \(\alpha \) -Stable benchmarks using likelihood-based information criteria and tail diagnostic tools. The empirical results show that the performance of TSPS varies across markets and sample periods. In samples where opening gaps exhibit shock clustering behaviour, the TSPS model provides additional explanatory power and a more informative decomposition of overnight risk. These findings suggest that the TSPS framework is best understood as a diagnostic distributional tool rather than as a uniformly dominant specification. Its practical relevance lies in connecting numerical tail fitting with interpretable risk components that may support overnight VaR and ES assessment, stress testing, and pre-opening risk monitoring.