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A transition matrix A representing probabilities of rating transitions during T years can be modified to model transition probabilities for a different time period Δ using iterative algorithm by Robert B.Israel, Jerry S.Rosenthal, and Jason Z.Wei ("Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit ratings", 2000). This algorithm provides raising the initial matrix to the power of Δ/T :
A_{Δ}=A_{T} ^{Δ/T} A simplified description of the algorithm is here. Our matrix power calculator matrixPower.exe with the input file and an example of the A_{T} matrix are free to use. Another implementation of this method is available in R. You can find the R code, the input data file, and an example of the output here. |