Modelling of Loan Non-Payments with Count Distributions Arising from Non-Exponential Inter-Arrival Times

Yeh-Ching Low () and Seng-Huat Ong
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Yeh-Ching Low: Department of Computing and Information Systems, Sunway University, Petaling Jaya 47500, Malaysia
Seng-Huat Ong: Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia

JRFM, 2023, vol. 16, issue 3, 1-14

Abstract: The number of non-payments is an indicator of delinquent behaviour in credit scoring, hence its estimation and prediction are of interest. The modelling of the number of non-payments, as count data, can be examined as a renewal process. In a renewal process, the number of events (such as non-payments) which has occurred up to a fixed time t is intimately connected with the inter-arrival times between the events. In the context of non-payments, the inter-arrival times correspond to the time between two subsequent non-payments. The probability mass function and the renewal function of the count distribution are often complicated, with terms involving factorial and gamma functions, and thus their computation may encounter numerical difficulties. In this paper, with the motivation of modelling the number of non-payments through a renewal process, a general method for computing the probabilities and the renewal function based on numerical Laplace transform inversion is discussed. This method is applied to some count distributions which are derived given the distributions of the inter-arrival times. Parameter estimation with maximum likelihood estimation is considered, with an application to a data set on number of non-payments from the literature.

Keywords: birth and renewal processes; loan default; non-payments; inter-arrival times; renewal function; over and under dispersion; Laplace transform (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
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