Bayesian Reliability Analysis Models And Bayesian State Space Models In Assessing Mortgage Default Risk

Capital allocation strategic decisions are made on the basis of creditworthinessassessment. In most aspects of bank’s portfolio, default is an extremely rare event andthe related data information is minimal. For the efficient allocation of capital, riskmanagement and the requirements of the Basel II frameworks on capital standards forbanks, inference about default rates is essential. In this paper, for one thing, we willintroduce duration-type models and their generalizations for modeling default risk,which are all based on the behavior of individual mortgages. We will use Bayesianmodeling method, which is applied for reliability or survival analysis, to describetime-related default data. About this part, our model is proportional hazards-typegeneralized gamma model, which is able to capture non-monotonic default rates.Besides, we also develop Bayesian inferences for this model. For another thing,according to the requirements of the Basel II rules, it’s crucial for banks and financialinstitutions to manage risk at the aggregate level. In modeling aggregate mortgagedefault rate, estimating if the rate exhibits a dynamic behavior and identifying effectof macroeconomic variables on the default rate are issues of consideration of bothresearchers and practitioners. In order to address these issues, we will introducediscrete time Bayesian state-space models with Poisson measurements to modelaggregate mortgage default rate. We will apply Markov chain Monte Carlo method(MCMC) to update and estimate parameters of the model. In assessing the dynamicnature of the mortgage default rate, we compare the forecasting behavior of theproposed models with a Bayesian Poisson regression model, which is as benchmarkmodel.