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.

The interest rate dynamics is an important fundamental for valuation more complex structures of interest rate derivatives. The goal of this diploma thesis is to describe the use of models of interest rate for interest rate option pricing. The paper could be logically divided into two parts, the theoretical one and practical one. In the first part the essentials for pricing theory are introduced as risk neutrality, martingales, stochastic differential calculus, and theory of arbitrage. On their basis four basic yield curve models are derived, Vasicek model, model Cox-Ingersoll-Ross , Black-Derman-Toy and two factor Heath-Jarrow-Morton model. Second part provides the analysis of yields of U.S. Treasury bonds with different maturity. At the end CIR model and BDT binomial tree are used for valuation of option on 10 years yield.