I am currently developing a loan default risk model using a discrete time hazard approach with xgboost. The goal is to generate a series of predicted monthly default probabilities using a new borrowers features at the time of origination.
The training data set contains monthly snapshots of each loan's payment history until the loan terminates via payoff or default. The data is set up as a binary classification problem with the target variable indicating if the borrower paid or defaulted that month. This indicator, plus the variable for loan age are the only time varying features in this data set. The rest are repeating features collected at the time of origination such as credit info and loan characteristics such as term length and loan amount.
The problem here is that some of the loans are right censored, so the loan history is not available for later months, especially for those that originated in recent years. What are some solutions to this problem? Should I remove the censored data?