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<p>A novel approach for estimating market risk, specifically focusing on Expected Shortfall (ES) and its alignment with the Basel III standard is introduced in this paper. The proposed model incorporates physics concepts of the Quantum Harmonic Oscillator (QHO) and applies time-dependent first-order perturbation theory. The study encompasses six selected capital markets within the European Union, including four developing markets and two highly developed and liquid markets. To construct the QHO model, empirical data on stock market returns over a three-year period were utilized. The wave function of the QHO, consisting of the ground state and the first nine excited states, served as the eigenfunction to accurately capture the empirical data. The research findings demonstrate the model’s reliability across both emerging markets and developed highly liquid markets. Furthermore, the results indicate that the proposed model generates more efficient estimates of ES compared to traditional GARCH models for assessing market risk.</p>

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The Potential use of a Quantum Oscillator for Estimating the Expected Shortfall: Case Study Selected Eu Countries

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Veljko Dmitrovic,
  • Vladimir M. Markovic,
  • Nenad Mitrovic,
  • Duško Petrovic,
  • Nikola Radivojevic

摘要

A novel approach for estimating market risk, specifically focusing on Expected Shortfall (ES) and its alignment with the Basel III standard is introduced in this paper. The proposed model incorporates physics concepts of the Quantum Harmonic Oscillator (QHO) and applies time-dependent first-order perturbation theory. The study encompasses six selected capital markets within the European Union, including four developing markets and two highly developed and liquid markets. To construct the QHO model, empirical data on stock market returns over a three-year period were utilized. The wave function of the QHO, consisting of the ground state and the first nine excited states, served as the eigenfunction to accurately capture the empirical data. The research findings demonstrate the model’s reliability across both emerging markets and developed highly liquid markets. Furthermore, the results indicate that the proposed model generates more efficient estimates of ES compared to traditional GARCH models for assessing market risk.