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?

  • 1
    $\begingroup$ You mean: equity value= a call option on the assets with a strike price equal to the debts. $\endgroup$ – dm63 Jan 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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.