Closed-form mortgage pricing formula with outstanding principal as prepayment value

This study considers all the possible actions a borrower may have, i.e., to default, to prepay, and to maintain the mortgage, during mortgage horizon. Then, we provide an effective and accurate pricing formula, which not only considers the effect that default might affect the mortgage value, but also more accurately explores the impact due to prepayment risk. In our model, we define prepayment value of the mortgage as the amount of outstanding principle. In contrast, previous literature defines prepayment value as a constant proportion of maintaining value of the mortgage. Finally, based on closed-form pricing formula, we analyze the yield, duration and convexity of risky mortgage loan, providing a better framework for risk management.