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Tag Archive for ‘interest’

MORTGAGE DEFAULT RATES

December 16, 2009mortgageComments Off

The historic default rates on mortgages have been generally much lower than on other consumer and corporate loans. They have also generally remained low even when borrowers have significant levels of negative equity. There are a number of reasons why this should be the case:
People have to live somewhere. Negative equity represents an unrealized loss. There is no incentive to realize this loss provided the borrower can service the loan. The advantage of moving to cheaper rented accommodation has to be balanced against the disadvantages of defaulting. Bankruptcy avoidance. If a borrower defaults on a property with significant levels of negative equity they are likely to face bankruptcy proceedings. In addition to the stress and loss of assets that such proceedings bring they are also likely to make it impossible for the borrower to ever own their own property.
Long dated option. A mortgage can be viewed as a long dated option. Given long enough most property markets eventually recover, even though it may take years. Option holders do not simply throw away an option that is out-of-the-money for the simple reason that it also has a “time value”. Given the typical term of mortgages the time value is significant, particularly as the “premium” they have paid (the down payment) represents a significant portion of their accumulated savings.
The level of defaults in the UK rose sharply after the residential property market crashed in 1986. A close examination of the problem showed that many defaulters had not actually made any down payment on their mortgage. Instead the lending bank had sold indemnity policies to them issued by an insurance company. These policies protected the banks from the first 20% of losses. Having paid very little for the option and being well out-of-the-money borrowers had little incentive to stay current and simply dropped off the keys after moving out.
The actual losses experienced by banks were relatively modest and the insurance companies simply responded by increasing the premiums charged for these policies. Few banks went through formal bankruptcy proceedings and, in the absence of a central register of defaulters, borrowers were able to go to another bank and took out a new mortgage on a different property. It’s a wonderful world.

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Distribution assumption

November 20, 2009Distribution assumptionComments Off

Now that I have pointed out the shortcomings of the normal distribution assumption in quantifying price change distributions, I intend to develop an option pricing model based on this very assumption. There is method in such an apparently contradictory approach. Knowing the limitations of a theoretical model in advance may allow us to correct its deficiencies after the fact using empirical information extracted from real price data. This pragmatic approach, I submit, is quite different from the conventional theoretical approach to option pricing which revolves around a mathematically perfect formula not applicable in the real world.
There are other benefits from proceeding initially on the normal assumption. Perhaps most important, the reader will be able to directly compare the simplified option pricing model I’m going to develop from first principles with the “million dollar formula” that dominates options literature. Before attemping to construct this model, I would like to make a few observations on price distributions in general and discuss ways of expressing these distributions as succinctly as possible.

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