This paper reports our estimates of the Value at Risk using Monte Carlo simulations for which we developed a computer program. Our approach involves obtaining Monte Carlo parameters by fitting real historical data of different periods to probability distributions. We applied the algorithm to the WIG20 and mWIG40 stock indices, and performed simulations for the Value at Risk at 95% and 99% confidence intervals over six estimation periods ranging from 1 trading day to 250 trading days. This approach was evaluated using the percentage failures and the Kupiec Proportion of Failures test. Our results indicate that this method is highly influenced by the choice of past historical and estimation period lengths considered. Overall, we observed that the Monte Carlo computational scheme is a reliable method for quantifying VaR when parametrized well.