Over time, bonds are liable to move from one rating category to another. This is sometimes...
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Over time, bonds are liable to move from one rating category to another. This is sometimes referred to as credit ratings migration. Rating agencies produce from historical data a rating transition matrix. This matrix shows the probabiltiy of a bond moving from one rating to another during a certain period of time. Usually the period of time is one year. Below is a table giving a rating transition matrix produced from historical data by Standard and Poor's (S&P) In reality, this transition matrix is updated every year. However if assuming no significant change in the transition matrix in the future, then one can use the transition matrix to predict what will happen over several years in the future. In particular, one can regard the transition matrix as a specification of a Markov chain model. Answer the following questions (a) Classify the states of ratings (transient or recurrent). What ratings are absorbing states? (b) Determine the classes of communicating states. (e) What is the probability that a currently "AAA" rated bond becomes default after 4 years? (d) Now consider what will happen in the long run, assuming that the transition matrix above operates every year. In the long run, what fraction of bonds are in "AAA"? and what fraction of bonds are in default? Over time, bonds are liable to move from one rating category to another. This is sometimes referred to as credit ratings migration. Rating agencies produce from historical data a rating transition matrix. This matrix shows the probabiltiy of a bond moving from one rating to another during a certain period of time. Usually the period of time is one year. Below is a table giving a rating transition matrix produced from historical data by Standard and Poor's (S&P) In reality, this transition matrix is updated every year. However if assuming no significant change in the transition matrix in the future, then one can use the transition matrix to predict what will happen over several years in the future. In particular, one can regard the transition matrix as a specification of a Markov chain model. Answer the following questions (a) Classify the states of ratings (transient or recurrent). What ratings are absorbing states? (b) Determine the classes of communicating states. (e) What is the probability that a currently "AAA" rated bond becomes default after 4 years? (d) Now consider what will happen in the long run, assuming that the transition matrix above operates every year. In the long run, what fraction of bonds are in "AAA"? and what fraction of bonds are in default?
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Answer a The states of ratings are transient The ratings that are absorbing states are AAA and Defau... View the full answer
Related Book For
Financial Statement Analysis
ISBN: 978-0078110962
11th edition
Authors: K. R. Subramanyam, John Wild
Posted Date:
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