Problem bank

Problem 290 of 333EasyLinear AlgebraP290

Eigenvalues of a rating migration matrix

  1. A simplified credit model has three states: A, B and Default. The one-year transition matrix, with rows as the starting state in the order (A, B, D), is

    P=(0.900.080.0200.850.15001)P = \begin{pmatrix} 0.90 & 0.08 & 0.02 \\ 0 & 0.85 & 0.15 \\ 0 & 0 & 1 \end{pmatrix}

    There are no upgrades and default is absorbing.

    • What are the eigenvalues of PP?
    • What is the probability that a B-rated bond has not defaulted after 10 years?
    • For large nn, does the survival probability of an A-rated bond shrink like 0.9n0.9^n or like 0.85n0.85^n?