Abstract
With a view to develop a more realistic model for credit risk analysis in consumer loan, our paper addresses the problem of how to incorporate business cycles into a repayment behavior model of consumer loan in portfolio. A particular Triplet Markov Model (TMM) is presented and introduced to describe the dynamic repayment behavior of consumers. The particular TMM can simultaneously capture the phases of business cycles, transition of systematic credit risk of a loan portfolio, and Markov repayment behavior of consumers. The corresponding Markov chain Monte Carlo algorithms of the particular TMM are also developed for estimating the model parameters. We show how the transition of consumers’ repayment states and systematic credit risk of a loan portfolio are affected by the phases of business cycles through simulations.
Highlights
Model (DCMM), as important extension to the simple MM, has been popular in credit modeling in recent years
One of the paths is that the transition consumers’ repayment behavior is directly a ected by the business cycle. e other path is the business cycle a ects the transition of systematic credit risk state of the loan portfolio and a ects the transition of consumers’ repayment behavior
One of the paths is that the transition of consumers’ repayment state is directly a ected by the business cycle. e other path is indirect impact, where the business cycle a ects the transition of systematic credit risk state of the loan portfolio, and a ects the transition of consumers’ repayment state
Summary
We present the structure of our particular TMM. For ease of comprehension and comparison, we rst introduce two simpler models: HMM and DCMM. HMM proposed in Baum and Petrie [20] has been widely used in various problems [21,22,23] It consists of two stochastic processes and , where is a Markov chain and not directly. E TMM extends DCMM by adding a discrete value process , such that the triplet , , is a Markov chain. ∈ ( ), ∈ ( ), ∈ ( ), transition probabilities between successive outputs given speci c input value and hidden state. We can see that the transition process of and depends on the speci c value of input variable and are all non‐homogeneous
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