Write about prepayment rate of a mortgage. Access mortgage database from fanni mae website and include Matlab or R codes in your work.

**Subject Business Mathematical Finance**

Write about prepayment rate of a mortgage. Access mortgage database from fanni mae website and include Matlab or R codes in your work.

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Introduction

Despite the 2008 economic crisis, housing remains the single most im- portant asset for most American families. The mortgage industry is full of literature that tries to explain the behaviour of the lenders (financial ins- titutions) the home sellers and the mortgagors or home buyers. The total outstanding size of the mortgage market is 2.7 trillion dollars. Between 1980 and 2005, the mortgage delinquency rate (defined to be loans past-due 60 days or more, plus foreclosures) averaged just over 2 percent. With the fi lien mortgage delinquency rate in 2010 at nearly 11 percent, much of the research focus on mortgage loan performance has shifted to default risk several factors have to be taken into account.

In the past, several authors have proposed models of rational mortgage prepayment based on contingent claims pricing theory. Dunn and McConnell modelled the optimum prepayment strategy of a mortgage holder when there is no prepayment costs. In all these models, there are four empirical features that appear :

1. Seasonality - this reflects the fact that the mortgage prepayment rate depends on the time of the year. For example, May - August and Sep- tember - April have diff t behaviours.

2. A burn-out factor

3. The mortgage holder does not always exercise option to prepay, even when optimum - Some mortgages are not prepaid even if the coupon rate may be above the current mortgage rate and vice versa, some mortgages are prepared even if their coupon rate may be below the current mortgage rate.

4. Risk factor - that is the risk associated to the market as well as the mortgager. Very often, it can be triggered by a life event or a market event....

Despite the 2008 economic crisis, housing remains the single most im- portant asset for most American families. The mortgage industry is full of literature that tries to explain the behaviour of the lenders (financial ins- titutions) the home sellers and the mortgagors or home buyers. The total outstanding size of the mortgage market is 2.7 trillion dollars. Between 1980 and 2005, the mortgage delinquency rate (defined to be loans past-due 60 days or more, plus foreclosures) averaged just over 2 percent. With the fi lien mortgage delinquency rate in 2010 at nearly 11 percent, much of the research focus on mortgage loan performance has shifted to default risk several factors have to be taken into account.

In the past, several authors have proposed models of rational mortgage prepayment based on contingent claims pricing theory. Dunn and McConnell modelled the optimum prepayment strategy of a mortgage holder when there is no prepayment costs. In all these models, there are four empirical features that appear :

1. Seasonality - this reflects the fact that the mortgage prepayment rate depends on the time of the year. For example, May - August and Sep- tember - April have diff t behaviours.

2. A burn-out factor

3. The mortgage holder does not always exercise option to prepay, even when optimum - Some mortgages are not prepaid even if the coupon rate may be above the current mortgage rate and vice versa, some mortgages are prepared even if their coupon rate may be below the current mortgage rate.

4. Risk factor - that is the risk associated to the market as well as the mortgager. Very often, it can be triggered by a life event or a market event....

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