Nonparametric Expectile Shortfall Regression for Complex Functional Structure

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.