SUMMARY
This study clarifies, the concepts of certain national debt with respect to the contingent debt as well as it identifies his impact in the sustainability ofthe public finances ofthe country. The reasoning that become about the sustainability ofthe debt, that is to say, if the debt of a country can be granted without a great future correction in the balance of income and expenses, go to determine in what moment a country is appropriate to refinance and when a reconstruction of the debt can be necessary. In the following part, an analysis is made on the uncertainty around the projections ofthe debt and the service ofthe debt, which is related to the contingent rights, such as the defined ones with the explicit or implicit guarantees ofthe debt or the contingent pensionales liabilities. Under the approach of the contingent rights in a added level, the mentioned points ofuncertainty are analyzed. We consider the risk of credit of the central goverrunent in this case (probability of default), evaluating the potential costs of the transferences and calculating spread on the national debt. Later it is examined the structure and operation del Colombian pensional system at the present time, evaluating multiple factors ofrisk that affect the scene as much ofthe Colombian system ofpensions today as in the future. Finally, with base in a range of teclmical alternatives of valuation of the risk and its implementation for the scene of the social security the problematic one of the risk acquires knowledge that locks up the pensional debt in variable Colombia projecting key like: the wage, the quotations, the employment and the GDP. With base in these projections, one analyzes the fiscal cost and the viability of the guarantee ofminimum pension.