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