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\title{Credit Risk Modeling: Default Probabilities}
\author{Jaime Frade}
\date{\today}

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\chapter*{Acknowledgments}
I would like to thank Dr. Niu for helping me learn the capabilities to incorporate statistical models and computational techniques in the real world.  The foundations and principals in this paper are largely due to his instruction and guidance.  I would also like to thank my family and friends for supporting me when I my hard drive crashed and I lost all my data and this paper.   They helped me to stay focus and build this from scratch. 

I would also like to thank my supervisor, Kevin Ceurvorst, and colleague, Ken Hill, at Florida State Board of Administration.  They helped me to combine my statistical and computational capabilities with their financial knowledge to produce the models in this paper. They provided guidance and critical ideas that helped me in this paper's model building process.  


\begin{abstract}
In this paper, the main objective is to build a quantitative model that estimates the probability that a US issuer will default on public debt within a year, as a function of  predictors that include financial ratios and equity market variables. The model is structured to balance timeliness and stability, and also allow company- or industry-level qualitative analysis.

The basic output of the model is a 1 year horizon forward estimate of default probability.  The model is uses logistic regression to derive the risk of insolvency within a year as a function of financial and market ratios. The steps taken in this paper are as follows:
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\begin{itemize}
\item Determine a logistic regression model
\item After determining a statisitcally significant model, will show how to estimate probabilities from current data and intepret a logit model.  
\item Discuss the significance and relationship of the variables. 
\item Comparsion of the model with other currently accepted models.  
\item Apply validation techniques.
\end{itemize}

The source language used to compile the model was SAS and Microsoft Excel.  Both programs were used for a confirmation of results.  Excel was also incorporated so that future usage by other analysts can be easily updated because of the lack of a SAS license.  Macros and programs in Excel were created and used in this paper that go along with the SAS results.


The goal of this paper was to build a statistical model that incorporate financial balance sheet items, which has been done in the past, but also to seek other market equity related variables.  The drive in this direction was mainly due to the recent high volatility in late 2008 of the credit arena. The months in late 2008 has experienced many companies defaulting on loans and disappear from the markets, such as Bear Stearns and Lehman Brothers.  Analyzing the market as a whole at this current time at the end of 2008, it is projected that many other companies may follow.  As of the date of this paper, General Motors and Chrysler Automotive companies are at headline risk.

In this paper, it was found that not all market variables are significant in a logistic regression model.  The two main models found that either   Market Equity over Total Assets (a measurement of \textbf{Leverage} ), 	Sales over Total Assets, (a measurement of \textbf{Competitiveness}), 	Earnings before Income Tax Adjusted	over Total Assets (a ratio that measures \textbf{Profitability}), and the last traded price of an issuer (the only market indicator)for that date were significant variables to predicting probabilities of default within a 1 year time horizon.  In this paper, the predications of the models are compared to other models that are currently accepted in the financial market as credit risk indicators.  Overall, there are high correlations between the statistical models and the models of this paper.  The logistic model can be used to predict default rates, however, more technical validation techniques need to me incorporated.  Also, depending on availability, more issuers that have defaulted may be added to the model.


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