Investigating the Performance of Alternative Default-Risk Models: Option-Based Versus Accounting-Based Approaches

Abstract

In this paper we evaluate the performance of three alternate default-risk models, seeking to find that measure which performs best, using a comprehensive sample drawn from the Australian equities market. The first two models are option-based models and are derived from Merton's (1974) insight that equity can be viewed as a call option on a firm's assets. In the first model, equity is modelled as a standard call option. In the second model, equity is modelled as a path-dependent barrier option. The third model is created using accounting ratios and is similar to Altman's (1968) Z-Score. To assess which of the models is superior, we consider variations of each model and then rely on prediction-oriented tests that focus on whether a firm subsequently defaults. Our results show that the option-based models clearly outperform their accounting ratio counterparts. Furthermore, our analysis suggests that the option-based models are very successful at ranking firms by default probability. It is noteworthy that the performances of the option-based models are difficult to distinguish from each other. The financial assistance provided by an ARC Linkage grant (LP0453913) and the helpful comments of an anonymous referee are gratefully acknowledged.-209 -(1974) that equity can be viewed as a call option on the firm's assets leads to a measure of default-risk that is derived from theory and is economically justifiable.In spite of the theoretical justification for the Merton model, Moody's-KMV, who are one of the leading providers of credit-risk measurement in the US, find that the Normal distribution underlying the Merton model understates the actual DP of firms. Using their own propriety dataset, collected over 20 years, Moody's-KMV observe that defaulted firms have a leptokurtic distribution. 1 Based on this finding, they have created their own propriety distribution, the EDF, to calculate DPs for firms. Researchers have latched onto this claim and argue that it is inconsistent to derive a formula for calculating DPs based on an underlying Normal distribution and then depart from this distribution in the final calculation of the DPs.Brockman and Turtle (2003) argue that path-dependent options rather than path-independent options, such as a standard call option, should be used to model equities and infer DPs for firms. The Merton model is path-independent because default can only occur if the asset value falls below liabilities at maturity. The asset value prior to maturity, or the 'path' followed by the asset value, does not affect the probability of default. Conversely, path-dependent options do take into consideration the asset value prior to maturity. One can argue that the path followed by the market value of assets prior to maturity is an important determinant of a firm's DP and hence that a barrier option is a more appropriate choice than a standard option for modelling equities. The relevant barrier option for equities is a down-and-out call (DOC) option on the firm's assets. With a DOC, the value of equity is zero if t...

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