The Meaning of Probability of Default for Asset-backed Loans

TL;DR

This paper clarifies the concept of probability of default for asset-backed loans, distinguishing between borrower failure and collateral insufficiency, and develops a framework to unify these definitions for consistent risk assessment.

Contribution

It introduces a mathematical framework that consistently applies and translates between two definitions of probability of default for asset-backed loans.

Findings

Defines two types of probability of default for asset-backed loans

Develops a mathematical model to unify these definitions

Enables consistent expected loss calculations across definitions

Abstract

The authors examine the concept of probability of default for asset-backed loans. In contrast to unsecured loans it is shown that probability of default can be defined as either a measure of the likelihood of the borrower failing to make required payments, or as the likelihood of an insufficiency of collateral value on foreclosure. Assuming expected loss is identical under either definition, this implies a corresponding pair of definitions for loss given default. Industry treatment of probability of default for asset-backed loans appears to inconsistently blend the two types of definition. The authors develop a mathematical treatment of asset-backed loans which consistently applies each type of definition in a framework to produce the same expected loss and allows translation between the two frameworks.