# Proper maturity in the Merton's model

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?

• You mean: equity value= a call option on the assets with a strike price equal to the debts. – 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.
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).