The Meaning of Probability of Default for Asset-backed Loans
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.