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.

翻译：风险价值（VaR）与条件风险价值（CVaR）已成为金融和保险领域最常用的市场风险度量指标。然而，这两种风险度量指标的估计极具挑战性，因为需要了解分布尾部特征。因此，通常采用极值理论工具，假设尾部数据服从广义帕累托分布（GPD）。基于基准分布参数与极限GPD参数之间的现有关系，我们定义了能整合全部观测值所有可用信息的高度信息性先验。针对指数分布、稳定分布和伽马分布情形，我们展示了如何运用高度信息性先验执行Metropolis-Hastings（MH）算法来估计VaR和CVaR。随后，我们开展了全面的模拟研究以比较三种不同方法的准确性与精确度。最后，通过实际数据案例的分析展示了这些方法的实践应用。