Interval Estimation of Transition Matrices Given Limited Data Sample

The problem of data limitations has become a crucially important concern since the advent of the computer era. The issue is especially relevant for risk management due to its high regulation by national and central banks as well as various standards (e.g. IFRS). The purpose of this thesis is, firstly, to advance an understanding of how limited data sample affects the estimates of probabilities of default and expected credit loss and, secondly, to identify cases when one could achieve higher estimate efficiency using the proposed methodology. The author analyses popular methodology based on Markov chains and migration matrices as well as reviews various methods of confidence estimation of matrix coefficients. The key methods of confidence estimation include Wald intervals, bootstrap and BMCMC. The author tests the adequacy of the methods as well as calculates the minimum number of observations (migrations) required to estimate migration probabilities at given accuracy level. Moreover, the paper proposes methodology for optimal portfolio segmentation to maximize the efficiency of the estimates. The thesis might be of interest for researches and analysts of credit risk and risk-management.