Considering the transition matrix below, what is the probability that a bond initially rated B will...

Considering the transition matrix below, what is the probability that a bond initially rated B will be in default (rating D) at the end of two years? Show how you derived your answer.

	A	B+	B	B-	C	D
A	0.94	0.03	0.02	0.01	0	0
B+	0.01	0.86	0.05	0.04	0.03	0.01
B	0.01	0.02	0.82	0.07	0.05	0.03
B-	0	0.03	0.05	0.78	0.06	0.08
C	0	0	0.06	0.06	0.7	0.18

Solutions

Expert Solution

We first fill the incomplete transition matrix noting that the sum of each column should be 1 (as it is a stochastic matrix)

So we get the transition matrix as

Based on this, we have

which is

The event of importance has probability given by the term

As this is in the column of B (third column) and the row of D (sixth row)

So the required probability is

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!

Colby Messinger answered 1 year ago

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