As a result of the credit crunch crippling the financial markets, a small retail bank wants to better predict and model the likelihood that its larger commercial loans might default. It is developing an internal rating-based approach to assess its commercial customers. A Markov chain model is used to predict the rating changes in the future and a one-year transition matrix is given below. For a loan with a current rating of B, list the various paths to default in years one, two and three. Then, calculate the respective probabilities of default. Rating Year 2 Rating Year 1 A A B C Default 90% 10% 0% 0% B 0% 75% 15% 10% C Default 0% 5% 55% 40% 0% 0% 0% 100%