| A mortgage model consists of three basic parts: the amortization model which examines the mortgage cash flows, the interest rate model which affects the mortgage price, and the prepayment model which measures the rates of mortgage termination when a property is sold, refinanced or foreclosed. A technique known as eigenfunction expansion has proven to be useful in pricing continuous-time mortgages.;The first part of this dissertation involves generalizing the existing mortgage model by analyzing the Cox-Ingersoll-Ross interest-rate model and including as an alternative the simpler Vasicek model and then comparing the results obtained by these methods. We also refine the relationship between interest rates and prepayments to reflect empirical data more accurately, particularly in low-interest rate scenarios by expanding the existing single-threshold prepayment model to include a secondary prepayment threshold.;The second problem expands the existing continuous prepayment model to include mortgage defaults. We use the default model to examine the price sensitivity of mortgages to loss severity and foreclosure rates. We also examine two practical applications of this model: accounting for wider spreads between mortgage yields and treasury yields during periods of economic stress, and estimating the value of the mortgage guarantee that government agencies such as Ginnie Mae provide to investors of mortgage-backed securities. |
