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Modeling Defaults in Residential Mortgage Backed Securities at Loan-Level

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Submitted By jjiang6
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1. Background Introduction
This paper looks into Cox Proportional Hazards model and constructs a mortgage default model to estimate the hazard rates of certain residential mortgage-backed securities (RMBS) on a loan-level basis. We analyze loans from an individual credit perspective instead of pool-level basis so that the model would closely fit each loan. This gives us the flexibility to adjust portfolio by observing individual loans and re-estimate their risks accordingly.

Ever since early 2000s, the issuance of residential mortgage-backed securities were steadily climbing due to the record-setting housing boom we have ever witnessed, then reached the peak at $1.2 trillion in 2005 and 2006, and finally became the center of attention during the crisis. Many investors have been trying to come up with newer and better models to monitor the default risk of RMBS ever since. Now that a majority of RMBS have been downgraded by credit-rating agencies since, it is necessary for investors to learn how to estimate the risk of their mortgage-backed securities to react to the adverse situation. We will skip the background of securitization and structure of mortgage-backed securities. In short, a pool of securitized mortgages gets divided into multiple tranches with different seniorities, ranging from AAA to equity. The higher the seniority goes, the lower risk and return the investors have, and they suffer losses after the lower seniorities do. Although investors look at a pool or tranches as a whole, each individual loan has its own level of risk. Understanding the credit risk of loans allows investors to adjust their portfolio according to their own risk appetites.
In this paper, we present Cox Proportional Hazards model to fit and estimate the defaults over the life of RMBS. We will introduce loan-specific factors that have impacts on a loan’s hazard rate. Once we are able to calculate the coefficients of each factor by running a series of regression tests, we can then determine their significances and insert/delete an optimal amount of factors in order to construct a better and more efficient default model. We hope that our model would assist those that are interested in predicting the risk of default of RMBS with accuracy and efficiency.

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