The purpose of this research is to implement the Bayesian quantile regression methodology in the estimation of the Value at Risk, VaR, in the colombian stock market. For this objective, some regulatory requirements on market risk are compared using the APARCH model, and traditional quantile regressions. These requirements are defined by the Colombia's Financial Superintendence where they address methodologies, performance measures and risk factors relevant to the calculation of the VaR. We found out that the later technique has a greater capacity to adapt to the patterns exhibited by a portfolio of Colombian stock given several performance measures.