Which of the following need to be assumed to convert a transition probability matrix for a given time period to the transition probability matrix for another length of time:

Which of the following need to be assumed to convert a transition probability matrix for a given time period to the transition probability matrix for another length of time:

I. Time invariance

II. Markov property

III. Normal distribution

IV. Zero skewness
A . I, II and IV
B . III and IV
C . I and II
D . II and III

View Answer

Answer: C

Explanation:

Time invariance refers to all time intervals being similar and identical, regardless of the effects of business cycles or other external events. The Markov property is the assumption that there is no ratings momentum, and that transition probabilities are dependent only upon where the rating currently is and where it is going to. Where it has come from, or what the past changes in ratings have been, have no effect on the transition probabilities. Rating agencies generally provide transition probability matrices for a given period of time, say a year. The risk analyst may need to convert these into matrices for say 6 months, 2 years or whatever time horizon he or she is interested in. Simplifying assumptions that allow him to do so using simple matrix multiplication include these two assumptions – time invariance and the Markov property. Thus Choice ‘c’ is the correct answer. The other choices (normal distribution and zero skewness) are non-sensical in this context.