The aim of this thesis is to model fully collateralized exposures in the presence of the Margin Period of Risk, i.e., the time between the last successful collateral call to the time where the amount of the loss crystallizes. We start with introducing a closed-form expression to model fully collateralized exposures for fixed versus floating interest rate swaps. Then the Brownian bridge method is introduced and applied, which allows for improvements computational wise. Finally, fully collateralized exposures are modeled in the presence of the Margin Period of Risk, with the Least Squares Monte Carlo method in the case of one European call option under Black-Scholes assumptions.