Academic journal article Journal of Financial Management & Analysis

Estimating Expected Default Probabilities Using the Option Pricing Model

Academic journal article Journal of Financial Management & Analysis

Estimating Expected Default Probabilities Using the Option Pricing Model

Article excerpt


Since the 1960s, a considerable number of studies have focused on predictions of corporate failure. Most of these studies use accounting information of financial statements to identify whether or not an individual firm may fail in the near future. Beaver1 presented the first statistical evaluation to predict corporate failure by using financial ratios and univariate analysis. Following Beaver's study, Altman2 used multivariate discriminant analysis, in which the financial ratios of a samples of failed and non-failed firms are analyzed in order to decide which ratios could best discriminate between failed and non-failed firms. This method of using financial ratios for failure prediction continued strongly throughout the 1970s and into the early 1980s. Scott3 noted potential search bias in the variable selection technique used by Altman. From the 1980s, some studies (e.g. Zavgren4; BarNiv and McDonald5) developed the new methods of conditional probability models using logistic regression techniques. These methods place a set of financial ratios into independent variables and use dependent variables of zero and one to represent failed and non-failed firms, to predict the default probability. To forecast the Japanese firms' bankruptcy accurately, Toda6 used 59 financial ratios to find what ratios are applied. Then, Shirata7 tested these ratios again but got a poor result.

These two probability models are assumed to normal distribution. However, Sheppard8 discovered that this assumption might not be true given an inappropriate set of predictors of all variables. In addition, the last model did not adequately prove that the default probability is between zero and one. In Japan, firms traded publicly on the stock markets hardly went bankrupt until 1996. The number of failed firms has been increasing since then, but the ratio of failed and non-failed firms is still low; therefore, the dependent variable is distributed skew expectantly. In addition, Japanese companies usually use acquisition prices to indicate their market values when they value the assets, so that we can hardly catch the real firm values from their financial statements. Furthermore, most Japanese companies' financial statements are only announced once or twice a year, and using discriminant and logistic analyses to estimate default probabilities promptly and accurately are difficult.

Three Standard Approaches

In the 1990's, there are three standard approaches, CreditMetrics, CreditRisk+ and KMV to credit risk management. CreditMetrics' approach was published by JP Morgan in 1997. This approach estimates the forward of the changes in value of a portfolio of loan and bonds at a given time horizon. However the assumption of no market risk over a specified period seems unreasonable. CreditRisk+ was published by Credit Suisse in 1997 that applies an actuarial science framework to the derivation of the loss distribution of a bond and loan portfolio. Only default risk is modeled, not downgrade risk. The disadvantage of this model is ignoring migration risk so that the exposure for each obligor is fixed and does not depend on eventual changes in the credit quality of the issuer.

The KMV model of assessing default probabilities is based on the asset value model originally proposed by Merton9. Merton developed the mode for pricing corporate liabilities by using an option approach that was extended from the Black-Scholes model. The concept of the Merton model is that a firm defaults when its market value falls below the value of its debts or a certain given threshold level. In the KMV model, the default process is endogenous, and relates to the capital structure of the firm. Default occurs when the value of the firm's assets falls below some critical level. The KMV model assessed the default probability and called it the expected default frequency (EDF). This approach relying on the market value to estimate the firm's volatility that incorporates market information on default probabilities. …

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