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Michael Weidman

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10 Nov 2011 Credit Risk Modeling with MATLAB These are the supporting MATLAB files for the MathWorks webinar of the same name. Author: Ameya Deoras

Michelle-

These results are entirely consistent with how classification trees work. Simply rescaling each of the inputs by multiplying them with different coefficients should have no effect on the tree.

For exactly why this is, I'd recommend Breiman's book (which is referenced in the doc), but the short answer is that trees sort each predictor's observations and try a candidate split within each of the gaps. The tree will then select the split that gives the "best" splitting criterion (and that's an entirely different discussion). Scaling the predictor only serves to scale this process, but it doesn't fundamentally change the results.

As an example: suppose we have a simple set of obervations where the predictor has been measured at 1, 2, 4, and 10. The tree will try splits at 1.5, 3, and 7. Let's say that the "best" split is at 7.

Now we go ahead and rescale this input-- mulitply it by 100 or some other coefficient. Now, the tree tries splits at 150, 300, and 700, and it will still select the split at 700. Rescaling doesn't change anything.

Now, if we were to cleverly create _new_ predictors out of a well-chosen combination (linear or otherwise) of our existing predictors, then that certainly would change the tree's performance. For instance, make a 6th predictor in your X from Altman's coefficient's times your original X-- then you might get some interesting results.

19 Oct 2011 Credit Risk Modeling with MATLAB These are the supporting MATLAB files for the MathWorks webinar of the same name. Author: Ameya Deoras

Michelle -

I'm afriad that I don't understand what histograms will do for you in this case. One typically matches the "actual" outputs to the model's "predicted" outputs and compares the difference between them in some way to assess the model's performance. Confusion matrices, ROC curves, and other techniques are commonly used to do this. Histograms are not used because they can hide a lot of information. Consider this simple case of classifying data that can take values of either "1" or "2":

% The "actual" data:
Y = [1 2 1 2 2 1];
% The "predicted" data, arrived at through some model:
Y_Pred = [2 1 2 1 1 2];

Most would argue that this "model" is terrible: it has a 100% misclassification rate! In spite of this, hist(Y) and hist(Y_Pred) give the exact same plot.

That visualization concern aside, I think there is some confusion about how Bagging works. In this example, the "actual" ratings are Y, and every observation is used for training in some way. So, Y also represents the training ratings. One of the strengths of ensemble methods like Bagging is that it's not necessary to manually split the data into training and validation sets: you can have your proverbial cake and eat it, too. The out-of-bag errors in this case, though, have a special significance that is too much to explain here-- you should check the doc or (better yet) Breiman's original article for more details on that. Suffice to say, you should not use the OOB errors in the way that you seem to be using them here. If you're looking for the ensemble's predicted ratings, they are simply found by
Y_Pred = predict(b,X);

24 Sep 2011 Credit Risk Modeling with MATLAB These are the supporting MATLAB files for the MathWorks webinar of the same name. Author: Ameya Deoras

Philip: On the top of this page we list the required products to run this code. R2010b of MATLAB should be fine as long as you have all of the needed toolboxes as well.

Within this package is a README file that provides step-by-step instructions on how to define the data sources (which is what seems to be going wrong in your error message above), how to get a copy of the MCR, and when you might need to recompile the code. I'm always looking for ways to improve those instructions, so let me know where you find them lacking.

15 Sep 2011 Credit Risk Modeling with MATLAB These are the supporting MATLAB files for the MathWorks webinar of the same name. Author: Ameya Deoras

That's useful feedback, Michelle. I've taken it back to our development team, and we're looking into incorporating those suggestions. Thanks!

14 Sep 2011 Credit Risk Modeling with MATLAB These are the supporting MATLAB files for the MathWorks webinar of the same name. Author: Ameya Deoras

Kostas: You're basically correct. PRBYZERO quotes clean prices; to worry about the partial coupon period, you'd need to use a dirty price convention or (equivalently) calculate the accrued interest. The ACCRFRAC function is useful in this case, as is the (more robust) BONDBYZERO function within Financial Derivatives Toolbox.

You're also correct that our choice of clean or dirty prices doesn't really affect the result as long as we're consistent: if present, the accrued interests from the original bond prices and the simulated bond prices just end up cancelling each other out.

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