Evaluate of the Merton Model for credit risk analysis
The KMV-Merton model proposed by Robert Merton(1974)is an application of classic option pricing theory and as a logical extension of the Black-Scholes(1973)option pricing framework.Merton’s approach assess the credit risk of a firm by characterizing the firm’s equity as a call option on the underling value of the firm with a strike price equal to the face value of the firm’s debt and a time-to-maturity of T.By put-call parity,the value of the firm’s debt is equal to the value of a risk-free discount bond minus the value of a put option written on the firm with a strike price equal to the face value of debt and a time-to-maturity of T.
To some extent,our calculated probability of default is reasonable.In fact,dynamics of default probability comes mostly from the dynamics of the equity values.KMV model can always quickly reflect deterioration in ...view middle of the document...
However there are also some weaknesses of this approach that may lead to the inappropriate probability of default.Our estimation of probability of default requires subjective estimation of the input parameters.We estimate volatility of equity from historical stock returns data and thus the market value and volatility of the firm’s asset,assuming one year forecasting horizon.Because only the price of equity for most public firms are observable,this model cannot be used by private firms.Instead,another model called RiskCalc can be applied by private firms which makes use of robust relationships between characteristics of private firms and the probability of default.The performance of Merton model in predicting default also depends on how realistic its assumptions are.It is difficult to construct theoretical default probability without the assumption of normality of asset returns and the too simplistic capital structure of the firm.(ie,value of firm=value of equity+value of debt)
In practice, we can only hope to estimate probabilities of default. That is, we will not be able to definitively classify firms into will default and will not default categories. As a result, in assessing the performance of a model, we face the task of assessing its ability to discriminate between different levels of default risk.As argued by Bharath and Shumway(2008),the probability of default implied by the Merton model is insufficient statistic for forecasting bankruptcy.They presented a “naive”application of Merton model that outperformed the complex application of Merton model.Also,The KMV model is static,meaning that once the debt is in place the firm does not change it. The default behavior of firms that manage their leverage positions is not captured.
Despite these limitations,the Merton model is being extensively used by Moody,S&P and other credit rating agencies worldwide for assessing the default probability of borrowing firms.This is because option-pricing models in bankruptcy prediction can provide guidance about the theoretical determinants of bankruptcy risk and necessary structure to extract bankruptcy-related information from market prices.