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<p>In this study, we explore an alternative pathway for financial risk assessment by leveraging the Rayleigh distribution to compute closed-form solutions for two pivotal risk quantifiers: Value at Risk (VaR) and Expected Shortfall (ES). Departing from the conventional reliance on normality assumptions, the proposed methodology embeds these expressions within the GARCH(1,1) modeling framework, offering a streamlined and analytically tractable risk evaluation approach. To validate the framework, we conduct empirical analyses on real-world stock data using one-step-ahead risk forecasts. Parameter estimation is achieved through maximum likelihood techniques, ensuring the reliability of model calibration.</p>

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Risk quantification using Rayleigh-Tail modeling framework: a theoretical study and numerical simulations

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Tao Liu,
  • Bolin Ding,
  • Fazlollah Soleymani

摘要

In this study, we explore an alternative pathway for financial risk assessment by leveraging the Rayleigh distribution to compute closed-form solutions for two pivotal risk quantifiers: Value at Risk (VaR) and Expected Shortfall (ES). Departing from the conventional reliance on normality assumptions, the proposed methodology embeds these expressions within the GARCH(1,1) modeling framework, offering a streamlined and analytically tractable risk evaluation approach. To validate the framework, we conduct empirical analyses on real-world stock data using one-step-ahead risk forecasts. Parameter estimation is achieved through maximum likelihood techniques, ensuring the reliability of model calibration.