Extending Entropic Value at Risk Using the γ-Order Generalized Normal Distribution

This paper extends the Entropic Value at Risk by considering the γ-order Generalized Normal distribution, a flexible family of distributions capable of modeling deviations from the classical normality assumption. An analytic expression for the Entropic Value at Risk is derived, and it incorporates a shape parameter γ that controls tail behavior and allows the model to capture heavy-tailed financial data more accurately. An empirical application to daily stock returns shows that this risk measure provides estimates closer to the empirical risk than those obtained under the normality assumption.