Yashkir Consulting

Financial Applications



Lasers & Matter



Transition matrices

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 simplified description of the algorithm is here.

Our matrix power calculator matrixPower.exe with the input file and an example of the AT matrix are free to use.

Download these three files into the same directory of your computer and run the power calculator. Resulting matrix will be created in the output file (see an example).

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.