Stress Testing Mortgage Defaults with Macro Factors and Hazard Spreads
Summary
The document considers estimating mortgage portfolio default probabilities under a two-year stressed macroeconomic scenario, using quarterly observations of one-year realized default rates and macroeconomic time series over a decade. The questioner describes a proposed workflow: transform series toward stationarity, screen macro variables for correlation, use stepwise selection for a linear regression, then fit an ARIMA model with selected exogenous variables. They report that this approach produced unreasonable stressed predictions across several portfolios and ask about alternatives.
The response suggests modeling spreads added to implied hazard rates as functions of macroeconomic factors, then calculating spreads under the stressed factors. This provides a compact scenario-mapping idea, but the document gives no implementation details, model specification, validation results, or comparison with the proposed methods. The brief sample and uncertain relevance of candidate predictors remain central constraints; the suggestion alone does not establish that stressed estimates will be stable or economically plausible.
Key ideas
- The task is to estimate mortgage default probability under a prescribed stressed macroeconomic path.
- The proposed baseline uses macroeconomic predictors with regression and ARIMA modeling.
- The answer suggests regressing spreads over implied hazard rates on macroeconomic factors.
- Under stress, the fitted spread relationship can be evaluated at the stressed factor values.
- The document provides no empirical validation or detailed guidance for this method.
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Full text
# Stress Testing Methods # Stress Testing Methods I'm working on the following task: > Given quarterly data: a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages a slew of realized (10 years of data) macroeconomic time series. Each time series may or may not be relevant A stressed scenario of those same macroeconomic time series for 2 years Estimate the probability of default using the stressed data. I don't actually know anything about underlying distributions. The only data I have for inference are these time series. My initial approach was something like this: I would first make every time series stationary. Then eliminate macroeconomic variables that were not significantly correlated with my dependent variable. Then use a stepwise method to determine the best variables to use in a linear regression. Then I would include those exogenous variables while fitting an ARIMA model. Along the way I would do several tests (e.g., autocorrelation, multicollinearity, stationarity, etc.). Then use that model for prediction. Note that I actually have several different "portfolios" which I am fitting. Using my above procedure, some of the stressed scenarios appear unreasonable. So, I began looking for totally different alternatives. Are there any suggestions? I realize this is an unreasonably broad question. To narrow the scope, I've done some brief research and believe some viable alternatives might include: - Calibrating some dynamic transition densities using Bayesian inference and MCMC - Calibrating a conditional Vasicek model that allows of autocorrelation The problem is, I'm not too familiar with these methods and would want to make efficient use of my time. Would you suggest I attempt implementing these alternatives? Or some other alternative? Do you have any advice for implementation in R? Thank you! ## Answer by user7056 (score 3) https://quant.stackexchange.com/a/14442 I would suggest you to add spreads to the implied hazard rates, spreads that you regress on the macroeconomic factors. Then you stress by calculating the spreads corresponding to the stressed factors.
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