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Stefan Tolls thesis consists of three self-contained essays.
Essay 1 examines the question of why reverse or participating
mortgages have not been as muck 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 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 necesserily increase. Furthermore,
as a special case, it is shownthat 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.
Essey 2 analyzes the effect of taxes on the the effect of
taxes on the optimal interest rate contract, aggregate tax income
and risk behavior. Using the optimal interest rate derived by Edelstein
and Urosevic (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 resaults are then applied
to a capital tax rate regime. We find that under the common income
tax rate regime, the effects 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 borrowerr´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
taxrates can, for some interest tare 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
valid default distribution. Two models emerge, one more flexible
with a zero recovery rate and one less flexible with a strictly
positve recovery rate. Assuming a common exponential decay parameter
for the term structure of credit and risk free interest rate instuments,
the conditions turn out to be interpretable andeasily verifiably.
The two models have been applied to Swedish mortgagge 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.
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