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.