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Value at Risk (VaR) and Conditional Value at Risk (CVaR) have become the mostpopular measures of market risk in Financial and Insurance fields. However, theestimation of both risk measures is challenging, because it requires theknowledge of the tail of the distribution. Therefore, tools from Extreme ValueTheory are usually employed, considering that the tail data follow aGeneralized Pareto distribution (GPD). Using the existing relations from theparameters of the baseline distribution and the limit GPD's parameters, wedefine highly informative priors that incorporate all the information availablefor the whole set of observations. We show how to perform Metropolis-Hastings(MH) algorithm to estimate VaR and CVaR employing the highly informativepriors, in the case of exponential, stable and Gamma distributions. Afterwards,we perform a thorough simulation study to compare the accuracy and precisionprovided by three different methods. Finally, data from a real example isanalyzed to show the practical application of the methods.

New Bayesian method for estimation of Value at Risk and Conditional Value at Risk