Studies in Mortgage Pricing and Finance Theory

Sammanfattning: This thesis consists of three self-contained essays.Essay 1 examines the question of why reverse or participating mortgages have not been as much in demand as predicted. A theoretical framework is derived for evaluating the expected utility associated with a reverse or participating mortgage. The borrower is a risk averse utility maximizing agent who derives utility from both consumption and leaving a bequest. If the agent's preferences are such that the liquid assets will eventually run out if the agent lives sufficiently long, the use of a reverse or participating mortgage could increase the expected utility. As a special case, it is shown that consumption will decrease at the time of commitment, contradicting a common belief that consumption will necessarily increase. Furthermore, as a special case, it is shown that the borrower will not release liquid assets from the real estate to such an extent that the borrower does not risk consuming all liquid assets, if the borrower live sufficiently long.Essay 2 analyzes the effect of taxes on the optimal interest rate contract, aggregate tax income and risk behavior. Using the optimal interest rate contract derived by Edelstein and Urošević (2003), which shares the total interest rate risk between a possibly risk averse lender and a strictly risk averse borrower, we add taxes under a general tax regime. The results are then applied to a capital tax rate regime and a common income tax rate regime. We find that under the common income tax rate regime, the effect of taxes is similar to a change in the borrower's risk aversion coefficient, but under the capital tax rate regime, the tax will change the borrower's income effect on the optimal interest rate contract. A progressive tax is then introduced and analyzed, resulting in potential kinks in the optimal interest rate contract. Furthermore, differences in tax rates can, for some interest rate contracts, be used to decrease the variability in aggregate tax income and as a policy tool to make lenders' risk taking costly.Essay 3 makes an effort to bridge the gap between the not uncommon industry practice to use the Nelson and Siegel model for modeling the term structure of credit interest rate instruments, and the conditions that must be fulfilled for this to result in a valid default distribution. Two models emerge, one more flexible with a zero recovery rate and one less flexible with a strictly positive recovery rate. Assuming a common exponential decay parameter for the term structure of credit and risk free interest rate instruments, the conditions turn out to be interpretable and easily verifiable. The two models have been applied to Swedish mortgage and governmental bonds between the end of 1993 and the end of 1999. The model with a strictly positive recovery rate is a priori preferable from an economic point of view but the results show the zero recovery rate with its greater flexibility to be preferable. We therefore conclude that the zero recovery rate model is a more appropriate way of modeling the default structure of issuers of defaultable interest rate instruments without option features.