An improved multivariate Markov chain model for credit risk

A simplified parsimonious higher order multivariate Markov chain model with new convergence condition

“…Transform (6) into a minimization problem: With the same process in [10], TPHOMMCM-NCC can be transformed into following form:…”

“…Markov chains is an important implement in many research areas, such as, internet applications [2] music [3], software testing [4], land cover change [5], energy consumption [6], speech recognition [7], physics, gene expression [9], finance [10][11], DNA [12] and so on. It is helpful to develop a better model for a more accurate prediction.by exploring the relationships of different categorical data sequences is meaningful to accurate prediction.…”

“…Numerical experiments illustrate the effectiveness of TPHOMMCM-NCC. Different methods for multiple categorical data sequences prediction (which means the relationships of different categorical data sequences are taken into account) has been proposed, e.g., the first-order multivariate Markov chain model, higher-order multivariate Markov chain model and an improved multivariate Markov chain model (to speed up the convergence) [10]. (They add a negative association part which is multiplied a constant for normalizing solutions at the back of the positive association part of the model.…”

A Flexible Markov Chain Approach for Multivariate Credit Ratings

“…We illustrate the practical implementation of the proposed model using real ratings data. We evaluate risk measures, such as Value at Risk and Expected Shortfall, for a credit portfolio using the proposed model and compare the risk measures with those arising from Ching et al (2007), Siu et al (2005). This paper is structured as follows.…”

“…More specifically, the influence from intra-transitions in an entity is random while that from cross transitions between any pair of entities is deterministic. This gives a more flexible dependent structure for ratings than Ching et al (2007). The number of parameters in the proposed model is of the magnitude O(sm(m + s)).…”