Modelling Credit Risks Using Unbounded Transitional Matrices

Abstract

Credit Risk management are ways of mitigating losses by considering the Bank’s capital adequacy and reserves for loan losses and it is a challenging process for most banking institutions. In many inputs of Risk management, Credit Migration matrices or Transition Matrices are the main inputs. In this Thesis, conditions for existence of a true generator in instances where the transition matrix is unbounded is identified for a Markov transition ma trix empirically observed. The Thesis comes up with generators which are valid and singles out the correct one compatible with the Credit rating be haviours and demonstrates how to obtain a generator which is approximate when a true generator is non existence especially in unbounded transitional matrices. Illustrations are given using secondary data gotten the standard and Poors website. The main challenge in transition matrices is in obtaining the generator matrix ˆ Q for ˆ P such that the exponential of ˆ Q will yield ˆ P. This challenge is known as embedding problem and is mostly experienced in Matrices higher than 3 by 3 square matrix. This problem is addressed where four statistical methods that use generator matrices to generate tran sitional matrices are proposed. They are the Diagonal and Weighted adjust ment method, the Generator Quasi-Optimization method, the EM algorithm method and finally the Gibbs sampler also known as the Markov Chain Monte Carlo method. The Credit data is analysed using the four methods and the best perfoming method gotten from comparison using the L-norm.