Range Based Risk Measures and Their Applications

We propose a family of range based risk measures to generalize the role of Value at Risk (VaR) in the formulation of Range Value at Risk (RVaR) considering other risk measures induced by a tail level. We discuss this type of measure in detail and its theoretical properties and representations. Moreover, we present a score function to evaluate the forecasts of these measures. In order to present the proposed concepts in an applied way, we performed illustrations using Monte Carlo simulations and real financial data