Abstract—Monotonic estimation for the survival probability of a loan in a risk-rated portfolio is based on the observation arising, for example, from loan pricing that a loan with a lower credit risk rating is more likely to survive than a loan with a higher credit risk rating, given the same additional risk covariates. Two probit-type discrete-time hazard rate models that generate monotonic survival probabilities are proposed in this paper. The first model calculates the discrete-time hazard rate conditional on systematic risk factors. As for the Cox proportion hazard rate model, the model formulates the discrete-time hazard rate by including a baseline component. This baseline component can be estimated outside the model in the absence of model covariates using the long-run average discrete-time hazard rate. This results in a significant reduction in the number of parameters to be otherwise estimated inside the model. The second model is a general form model where loan level factors can be included. Parameter estimation algorithms are also proposed. The models and algorithms proposed in this paper can be used for loan pricing, stress testing, expected credit loss estimation, and modeling of the probability of default term structure.
Index Terms—Loan pricing, survival probability, cox proportion hazard rate model, baseline hazard rate, forward probability of default, probability of default term structure.
Bill Huajian Yang is with Royal Bank of Canada, Canada (e-mail: email@example.com).
Cite: Bill Huajian Yang, "Monotonic Estimation for the Survival Probability over a Risk-Rated Portfolio by Discrete-Time Hazard Rate Models," International Journal of Machine Learning and Computing vol. 9, no. 5, pp. 675-681, 2019.Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).