Mortgage backed securities are one of the most important asset classes available to fixed income investors. They are also essential to the functioning of the financial and housing market by providing liquidity to the home mortgage market. Proliferation and wide spread acceptance of mortgage backed securities resulted in a significant deduction of the interest rates for home mortgages. The 2007-2010 financial crisis sparked enhanced scrutiny of the accuracy of the pricing of mortgage backed securities. The purpose of the present thesis is to develop a computer based mathematical methodology to accurately price individual mortgages that are the fundamental assets underlying every mortgage backed security. The focus of this paper is to correctly account for inherent interest rate and prepayment risk. Default risk is not subject of this project. Interest rate risk is handled in the framework of the arbitrage free Black-Derman-Toy (BDT) model. Public Securities Association’s (PSA) model is used to simulate prepayment risk. Monte Carlo simulation methodology is developed to evaluate the properly discounted current value of the risky cash flows and hence value the mortgages. The computational algorithms are implemented in R.