SUMMARY
Credit Risk is an important dimension to be considered in the risk management procedures of financial institutions. Is a particularly useful in emerging markets where default rates on bank loan products are usually high. It is usually calculated through highly costly Monte Carlo simulations which consider different stochastic factors driving the uncertainly associated to the borrowers liabilities. In this paper, under some restrictions, we drive closed form formulas for the probability distributions of default rates of bank loans products involving a big number of clients. This allows us to quickly obtain the credit risk of such products. Moreover, using these probability distributions, we solve the problem of optimal portfolio allocation under default risk.