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Question 15 Over time, bonds are liable to move from one rating category to another. This is sometimes referred to as credit ratings migration. Rating agencies use historical data to produce a rating transition matlix. This matrix shows the probabiltiyr of a bond moving from one rating to another dining a certain period of time. Usually the period of time is one year. Table TJ. gives a rating transition matrix produced from historical data by Standard and Poorls (SEEP) in 2001. In reality, this transition matrix is updated every year. However, if we assume that there will be no significant change in the transition matrix in the future, then we can use the transition matrix to predict what will happen carer several years in the future. In particular, we can regard the transition matrix as a specication of a Markov chain model. Answer the following questions: {a} Classify the states of ratings {transient or recurrent}. 'What ratings are absorbing states? {h} Determine the clamm of communicating states. [no] 11.l'-.I'hat is the prlzllaatrilit},r that a currentlyr AAArated bond in default after four years? {d} Now consider what 1will happen in the long run, assuming that the transition matrix above operates every year. In the long run, what fraction of bonds are in state AAA? What fraction of hands are in default