Abstract
A Markov Chain model can be used to model loan defaults because loans move through delinquency states as the borrower fails to make monthly payments. The transition matrix contains in each location a probability that a borrower in a given state one month moves to the possible delinquency states the next month. In order to use this model, it is necessary to know the transition probabilities, which are unknown quantities. A Bayesian hierarchical model is postulated because there may not be sufficient data for some rare transition probabilities. Using a hierarchical model, similarities between types or families of loans can be taken advantage of to improve estimation, especially for those probabilities with little associated data. The transition probabilities are estimated using MCMC and the Metropolis-Hastings algorithm.
Degree
MS
College and Department
Physical and Mathematical Sciences; Statistics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Monson, Rebecca Lee, "Modeling Transition Probabilities for Loan States Using a Bayesian Hierarchical Model" (2007). Theses and Dissertations. 1249.
https://scholarsarchive.byu.edu/etd/1249
Date Submitted
2007-11-30
Document Type
Selected Project
Handle
http://hdl.lib.byu.edu/1877/etd2179
Keywords
MCMC, Hierarchical Model, multinomial, Dirichlet
Language
English