Abstract
The difficulty of pricing mortgages lies in the uncertainty of the cash flow and this uncertainty comes from the default and prepayment. The previous studies use only the stochastic processes of interest rate and house price to analyze the default and prepayment decisions and generate overestimated results for they ignore the household income can also affect the decisions. This study includes the household income process to analyze the default conditions of four types of mortgage, Fixed-Rate Mortgage, Price Level Adjusted Mortgages, Variable-Rate Mortgages, and Adjustable-Rate Mortgages, by Monte Carlo simulation and then compares the results in order to give some suggestions about choosing mortgages. The results show that the default probabilities which are generated from the simulation incorporating interest rate and house price only are overestimated. Although the default probability of FRM is the lowest of all, the banks issuing FRM must bear the whole interest rate risk. Therefore, ARM will be the appropriate mortgage for banks to release for it has a relatively low default probability and the borrowers have to share the interest rate risk with banks.