Links to all tutorial articles (same as those on the Exam pages)Credit Migration Framework
This is the first of five articles that provide a high level understanding of the various portfolio models of credit risk covered in the PRMIA syllabus. Being the first one, this discusses the credit migration framework. (I am still working on the others.) This article is intended to provide a conceptual understanding of the approach and I have not provided numerical examples for the reason that I don’t want to duplicate what is already there in the Handbook. Once you have read this, the scattered explanation in the Handbook will hopefully make more sense. The credit migration framework is based upon the knowledge of the future distribution of the credit ratings of securities, given a current known rating. We may know today that a bond is rated say AA, and we know from historical experience (collected and published by all major credit rating agencies) what the likelihood of this bond’s future rating is at the end of one year. For example, we may know today that the probability of this AA bond moving to a rating of BB is say 4%, and the probability of its staying at AA is 85%. Now if we know the credit rating of a bond, we also know what it is worth. How? Because bond prices for different ratings are observable in the markets. Based on this information, we can quite easily build a future distribution of an individual bond’s future prices. Now if we know the correlation between the credit migration (ie, the move from one credit rating to another) of the different bonds in the portfolio, we can generate a distribution of the future value of the portfolio, and thus calculate the portfolio VaR.
Step 2: Specify the one year forward zero curve for each rating class (assuming our risk horizon is one year, as is generally the case). What does a one year forward zero curve mean? This means the ‘zero curve’ from time = +1 (ie starting at the end of 1 year from now) to future years 1, 2, 3, 4 and so on; so that we can build an interest rate curve that is expected at the end of one year from now. We will use this interest rate curve to determine the value of the bond at the end of 1 year from now for each of the possible credit ratings it can assume in the future. Note that there will be a different curve for each rating class. Each curve will be applied to the coupons and final payment on the bond to determine its PV at the end of year 1 from now. Step 3: Using the probabilities from the transition matrix in Step 1, and the possible future bond values from Step 2, we get a distribution of future values of the bond. Note that if we know the possible future values of the bond, and the probability of its actually being at that value, we can quite easily calculate an expected value, or average. But that is not the point. What we want is the distribution so we can get our bottom 1% or 5%, or whatever level of confidence we are interested in as VaR.
Wait a second you might say – the last sentence makes no sense. Till a minute ago we were talking in an abstract sort of way about correlations between rating migrations, and suddenly we have introduced asset returns and return correlations. Let me explain that.
