A Mathematical Method for Deriving the Relative Effect of Serviceability on Default Risk

TL;DR

This paper introduces a mathematical method to quantify how a borrower's income relative to debt obligations influences default risk, considering income uncertainty over the loan's lifespan.

Contribution

It extends existing models by incorporating income uncertainty into risk weight calculations, providing a more nuanced assessment of serviceability's impact on default risk.

Findings

Serviceability may be underrepresented in mortgage risk models.

The method quantifies default probability based on income distribution.

Numerical examples demonstrate the importance of accounting for income uncertainty.

Abstract

The writers propose a mathematical Method for deriving risk weights which describe how a borrower's income, relative to their debt service obligations (serviceability) affects the probability of default of the loan. The Method considers the borrower's income not simply as a known quantity at the time the loan is made, but as an uncertain quantity following a statistical distribution at some later point in the life of the loan. This allows a probability to be associated with an income level leading to default, so that the relative risk associated with different serviceability levels can be quantified. In a sense, the Method can be thought of as an extension of the Merton Model to quantities that fail to satisfy Merton's 'critical' assumptions relating to the efficient markets hypothesis. A set of numerical examples of risk weights derived using the Method suggest that serviceability may be under-represented as a risk factor in many mortgage credit risk models.