Generating Transition Probability Matrices through an Optimization Framework

Abstract

Transition probability matrices (TPMs), which indicate the likelihood of obligor credit migration over a given time horizon, have been used in various credit applications ranging from pricing of financial instruments, loan evaluation, portfolio risk analysis, and economic capital assessment. The standard methodology for calculating TPMs is the discrete, cohort approach. We present an alternative method for calculating TPMs using an optimization methodology. The optimization framework incorporates multiple business requirements, such as: ensuring smooth surfaces with consistent probability mass distributions, reduction of impact from time homogeneity and Markov assumptions, and reduction of forecast errors for multiple time steps. The resultant optimized TPMs are compared with traditional discrete TPMs developed using the cohort method. The proposed optimization method results in TPMs with significantly better predictive power and properties that better suit many business applications.