I am working on a credit rating project using Merton's model. Basically it adopts Black-Scholes that equity value can be viewed as a call option with a strike price of face value of debts. Since the maturities of different debts vary and I have a long list of companies, choosing a proper maturity of debts for all is a difficult task. any good advice for the problem?

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    $\begingroup$ You mean: equity value= a call option on the assets with a strike price equal to the debts. $\endgroup$ – dm63 Jan 19 '19 at 0:29

The original Merton model takes a simplified view of the debt structure in assuming the total value of outstanding debt (or some portion thereof) $D$ matures at a specified time $T$. Shareholders are long a European call option on the firm value struck at the face value of debt and bondholders are long a risk-free zero coupon bond and short a European put option struck at the face value of debt. To implement the model the time to expiration of the options is taken as $T$.

Such assumptions about $D$ and $T$ appear to be vast oversimplifications of the capital structure of real firms. However, they can be handled in a way that may very well be useful depending upon the purpose for the model. It may be better to apply a simple, parsimonious model consistently. For example $T$ may be taken as the duration of the debt or even a fixed horizon with $D$ taken as some representative measure of the outstanding debt. Credit ratings and estimates of default probability are generally applied in a relative way across debt issuers in portfolio construction.

The firm KMV (acquired by Moody's) developed one of the first commercially available credit models providing estimates of default probability for a one-year horizon. The KMV approach is based on the Merton model in conjunction with calibration to historical data . With this enhancement, it is not necessary to be overly concerned with all details of the capital structure but rather to use a consistent simple specification that is amenable to calibration.

KMV found that the model was most effective by setting $D$ to be the sum of the total face value of short-term debt (maturing within a year) and one half of the total face value of long-term debt (maturing beyond a year).

The rationale for KMV's approach -- which makes a lot of sense -- is that default is driven more by the inability to service short-term debt because the issuer can often negotiate restructuring of long-term debt with greater flexibility.

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