# loan default model

I have a loan dataset that includes all the loans originated from 2000 through the most recent quarter. For each loan, available are information at origination, such as loan size, FICO, LTV, LTI etc... Also available is the monthly repayment information. Macroeconomic information is publicly accessible. Since loans were originated in different years, length of history could differ.

I am trying to predict each loan's probability of default(defined as 90 days past due) for each of the next 4 quarters, using 1) origination information, 2) repayment information, 3) macroeconomic information. That's to say I would like to calculate 4 probabilities for each loan, one for each quarter.

I thought of survival analysis but it doesn't seem to predict probability (hazard rate). It predicts cumulative hazard /hazard ratio. To model with logistic regression, each loan for each quarter would be a data point until the quarter when event (default) happens. multiple records for 1 loan would make the sample not independent.

Could anyone help or provide some thoughts? Thanks a lot.

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• You can use logistic regression for discrete time survival analysis (cf here) since you are only interested in quarters. Alternatively, you can integrate over the hazard to get the probability of default. – gung May 5 '15 at 19:05
• Thank you very much @gung! When use logistic regression, shouldn't the observations be independent? But with multiple observations for each, is independence violated? Also since loans have different # of records, do they need to be weighted in some way? Thanks a lot. – LFA May 6 '15 at 17:52
• If you estimate probability of defaulting in month n conditioned on not defaulting in previous months, then they are independent (as is done for discrete time survival analysis). – seanv507 Nov 13 '18 at 10:13

Using survival analysis, you compute the survival function $S(t)$, from which you can compute the probability of default. For example, if $S(t=\text{1 year}) = 0.9$ and $S(t=\text{2 year}) = 0.8$, you know that the probability of default during the second year of the loan is $0.8/0.9$.