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CRMM-6-default-risk-quantitative-methodologies.html
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<title>Credit Risk Measurement and Management | Chapter 6 | Default Risk: Quantitative Methodologies</title>
<meta name="description" content="Financial Risk Manager Part 2 Study Materials">
<meta name="author" content="MacLane Wilkison">
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<section>
<h1>Chapter 6</h1>
<h3>Default Risk: Quantitative Methodologies</h3>
<p>
<small>Created for <a href="http://alchemistsacademy.com">Alchemists Academy</a> by <a href="http://alchemistsacademy.com/about">MacLane Wilkison</a></small>
</p>
</section>
<section>
<h2>Assessing Default Risk Through Structural Models</h2>
<ul>
<li>Structural models describe the default process as the explicit outcome of the deterioration of firm value</li>
<li>Merton model - applies Black-Scholes option model to corporate securities</li>
<li>KMV credit monitor model - extracts implied probabilities of default at a given horizon from equity prices</li>
<ul>
<li>PD<sub>t</sub>=N[(logV<sub>t</sub>-logX+(μ-σ<sup>2</sup><sub>V</sub>/2)(T-t))/[σ<sub>V</sub>√(T-t)]]</li>
</ul>
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<aside class="notes">
The Merton model assumes: the capital structure is simplistic, the value of the firm is perfectly observable, the value of the firm follows a lognormal diffusion process, default can occur only at debt maturity, riskless interest rates are constant through time and maturity, no debt renegotiation between equity and debt holders, no liquidity adjustment. KMV model variables: N(.) = cumulative Gaussian distribution; V<sub>t</sub> = value of firm at time t; X = default threshold; σ<sub>V</sub> = asset volatitility of firm; μ = expected return on assets
</aside>
</section>
<section>
<h2>Credit Scoring</h2>
<ul>
<li>Characteristics of good scoring model:</li>
<ol>
<li>Accuracy</li>
<li>Parsimony</li>
<li>Nontriviality</li>
<li>Feasibility</li>
<li>Transparency and interpretability</li>
</ol>
<li>Major approaches</li>
<ul>
<li>Fisher linear discriminant analysis</li>
<li>Logistic regression and probit</li>
<li>k-nearest neighbor classifier (KNN)</li>
<li>Support vector machine classifier</li>
</ul>
</ul>
<aside class="notes">
1. low error rates attributable to model's assumptions; 2. not using too large a number of explanatory variables; 3. producing relevant/interesting results; 4. running in a reasonable amount of time and consuming realistic resources; 5. providing high-level insight into relationships and trends, as well as a clear understanind of how model output is generated. Linear discriminant analysis segments and classifies a heterogeneous population into homogeneous subsets. The KNN technique assesses the similarities between input pattern 'x' and a set of reference patterns from a training set. A pattern is then classified to a class of the majority of its k-nearest neighbor in the training set. Support vector machines analysis involves separating the various classes of data by drawing a "best-fit" hyperplane.
</aside>
</section>
<section>
<section>
<h2>Model Performance Measures</h2>
<ul>
<li>"Minimum-error" decision rule - uses Bayes' theorem to assign borrowers to a class with the goal of minimizing default probability</li>
<li>"Minimum-risk" decision rule - uses Bayes' theorem to assign borrowers to a class with the goal of minimizing expected loss</li>
<li>Neyman-Pearson decision rule</li>
<li>Minimax decision rule</li>
</ul>
</section>
<section>
<h2>Targeting Classification Accuracy</h2>
<ul>
<li>Reciever operating characteristic (ROC) approach - plots the number of correctly classified firms against the number of incorrectly classified firms</li>
<li>Gini/cumulative accuracy profile (CAP) approach - curve that assesses the consistency of the predictions of a scoring model to the ranking of observed defaults</li>
</ul>
</section>
<section>
<h2>Targeting Prediction Reliability</h2>
<ul>
<li>Maximum-likelihood decision rule - a measure of wealth maximization for the user of the scoring model</li>
<li>Goodness-of-fit tests - measure the deviation of a random sample from a given probability distribution</li>
</ul>
</section>
</section>
<section>
<h1>THE END</h1>
<h3><a href="http://alchemistsacademy.com">AlchemistsAcademy.com</a></h3>
</section>
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