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

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  • Graham Andersen
  • David Chisholm

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.

Suggested Citation

  • Graham Andersen & David Chisholm, 2011. "A Mathematical Method for Deriving the Relative Effect of Serviceability on Default Risk," Papers 1111.5397, arXiv.org.
  • Handle: RePEc:arx:papers:1111.5397
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    File URL: http://arxiv.org/pdf/1111.5397
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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
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