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Nonparametric Expectile Shortfall Regression for Complex Functional Structure.

Mohammed B Alamari1, Fatimah A Almulhim2, Zoulikha Kaid1

  • 1Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia.

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Summary
This summary is machine-generated.

This study introduces a new conditional expected shortfall risk metric using expectiles. This novel approach offers a practical and sensitive tool for financial risk management, outperforming standard methods.

Keywords:
complete consistencyexpected shortfallexpectile regressionfinancial riskfunctional datakernel methodquantile regresion

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Area of Science:

  • Quantitative Finance
  • Financial Risk Management
  • Statistical Modeling

Background:

  • Traditional risk management metrics like Value at Risk (VaR) have limitations in capturing tail risk.
  • Conditional Expected Shortfall (CES) is a more comprehensive risk measure, but its estimation can be complex.
  • There is a need for robust and easily implementable risk metrics in financial time-series analysis.

Purpose of the Study:

  • To introduce a new conditional expected shortfall (CES) function for enhanced risk management.
  • To develop a nonparametric estimator for this novel CES metric.
  • To demonstrate the practical applicability and sensitivity of the new risk metric using financial data.

Main Methods:

  • Definition of a new CES function using expectiles as the shortfall threshold.
  • Construction of a nonparametric estimator employing the Nadaraya-Watson approach.
  • Establishment of asymptotic properties using functional time-series analysis and concentration inequalities.
  • Validation through real and simulated financial time-series data.

Main Results:

  • A novel, nonparametric CES estimator is developed and its convergence rate determined.
  • The new risk metric demonstrates ease of implementation and sensitivity to financial time-series fluctuations.
  • Empirical studies confirm the feasibility of the proposed risk tool.
  • Comparative analysis shows advantages over standard shortfall measures.

Conclusions:

  • The proposed expectile-based CES function provides a valuable and practical advancement in financial risk management.
  • The nonparametric estimator is statistically sound and performs well on real-world financial data.
  • This new metric offers a more nuanced understanding of risk compared to traditional methods.