Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation

This research aims to determine the existence of inflection points when companies’ credit risk goes from being minimal (Hedge) to being high (Ponzi). We propose an analysis methodology that determines the probability of hedge credits to migrate to speculative and then to Ponzi, through simulations w...

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Main Authors: Nora Gavira-Durón, Octavio Gutierrez-Vargas, Salvador Cruz-Aké
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/9/8/879
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spelling doaj-23e4f8de23644af297723fbd553209b92021-04-16T23:01:32ZengMDPI AGMathematics2227-73902021-04-01987987910.3390/math9080879Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability EstimationNora Gavira-Durón0Octavio Gutierrez-Vargas1Salvador Cruz-Aké2Department of Banking and Investments, School of Business and Economics, Universidad de las Americas Puebla, Puebla 72810, MexicoHigher School of Economics, Instituto Politécnico Nacional, Santo Tomas Campus, Ciudad de México 11350, MexicoHigher School of Economics, Instituto Politécnico Nacional, Santo Tomas Campus, Ciudad de México 11350, MexicoThis research aims to determine the existence of inflection points when companies’ credit risk goes from being minimal (Hedge) to being high (Ponzi). We propose an analysis methodology that determines the probability of hedge credits to migrate to speculative and then to Ponzi, through simulations with homogeneous Markov chains and the k-means clustering method to determine thresholds and migration among clusters. To prove this, we used quarterly financial data from a sample of 35 public enterprises over the period between 1 July 2006 and 28 March 2020 (companies listed on the USA, Mexico, Brazil, and Chile stock markets). For simplicity, we make the assumption of no revolving credits for the companies and that they face their next payment only with their operating cash flow. We found that Ponzi companies (1) have a 0.79 probability average of default, while speculative ones had (0) 0.28, and hedge companies (−1) 0.009, which are the inflections point we were looking for. Our work’s main limitation lies in not considering the entities’ behavior when granting credits in altered states (credit relaxation due to credit supply excess).https://www.mdpi.com/2227-7390/9/8/879homogeneous markov chainsk-meanscredit riskdefault clusters
collection DOAJ
language English
format Article
sources DOAJ
author Nora Gavira-Durón
Octavio Gutierrez-Vargas
Salvador Cruz-Aké
spellingShingle Nora Gavira-Durón
Octavio Gutierrez-Vargas
Salvador Cruz-Aké
Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
Mathematics
homogeneous markov chains
k-means
credit risk
default clusters
author_facet Nora Gavira-Durón
Octavio Gutierrez-Vargas
Salvador Cruz-Aké
author_sort Nora Gavira-Durón
title Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
title_short Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
title_full Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
title_fullStr Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
title_full_unstemmed Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
title_sort markov chain k-means cluster models and their use for companies’ credit quality and default probability estimation
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-04-01
description This research aims to determine the existence of inflection points when companies’ credit risk goes from being minimal (Hedge) to being high (Ponzi). We propose an analysis methodology that determines the probability of hedge credits to migrate to speculative and then to Ponzi, through simulations with homogeneous Markov chains and the k-means clustering method to determine thresholds and migration among clusters. To prove this, we used quarterly financial data from a sample of 35 public enterprises over the period between 1 July 2006 and 28 March 2020 (companies listed on the USA, Mexico, Brazil, and Chile stock markets). For simplicity, we make the assumption of no revolving credits for the companies and that they face their next payment only with their operating cash flow. We found that Ponzi companies (1) have a 0.79 probability average of default, while speculative ones had (0) 0.28, and hedge companies (−1) 0.009, which are the inflections point we were looking for. Our work’s main limitation lies in not considering the entities’ behavior when granting credits in altered states (credit relaxation due to credit supply excess).
topic homogeneous markov chains
k-means
credit risk
default clusters
url https://www.mdpi.com/2227-7390/9/8/879
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AT octaviogutierrezvargas markovchainkmeansclustermodelsandtheiruseforcompaniescreditqualityanddefaultprobabilityestimation
AT salvadorcruzake markovchainkmeansclustermodelsandtheiruseforcompaniescreditqualityanddefaultprobabilityestimation
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