Entropic risk measure EVaR real data testing

Investigating risk measures is crucial for understanding and managing the uncertainties inherent in various financial and economic activities. Risk measures provide quantitative assessments of potential losses, enabling businesses and financial institutions to make informed decisions and mitigate adverse outcomes. The background of this research lies in the increasing complexity and interconnectedness of financial markets, which have increased the impact of risks and the need for robust risk management frameworks. Traditional measures, such as Value at Risk (VaR), have been widely used, but their limitations, particularly during financial crises, have highlighted the necessity for more comprehensive approaches like Expected Shortfall (ES) and Entropic Value at Risk (EVaR). The relevance of investigating risk measures is underscored by the financial turmoil experienced during global crises, such as the 2008 financial meltdown and the COVID-19 pandemic. These events exposed the vulnerabilities of existing risk management practices and underscored the need for more resilient and accurate risk assessment tools. The purpose of this research is to evaluate and compare different risk measures, providing insight into their strengths and weaknesses, and to develop more effective strategies for risk management. In the paper, we investigate the performance of the Entropic Value-at-Risk (EVaR) risk measure on real financial data, com- paring it with traditional risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We consider historical return data from the S&P 500 index and Bank of America Corp. shares (2009–2019) and apply various parametric models, including normal and Laplace distributions. We also employ standard backtesting methods (coverage and independence tests) to assess the empirical adequacy of these measures. Our analysis highlights the mathematical properties of EVaR and its ability to detect heavy-tailed behavior more effectively than VaR, while providing coherent and potentially more robust estimates in volatile market conditions. Future research perspectives include the development of new risk measures that can better capture systemic risks in financial markets. In addition, integrating machine learning and artificial intelligence with traditional risk measures presents an avenue to improve predictive accuracy and robustness. This ongoing research is important for building more resilient financial systems and for protecting economic stability.