Overview
The Merton model shows how the equity of a company can be viewed as a call option on the company's assets. In its simplest form, the company is modeled in a two period setting (see below). A continuous time model can also be formulated. (see continuous time merton)
Model
- Corporate Debt
The company begins with an amount of debt, which is given by a function {% D(t) %}. The value of the initial debt is
then {% D(0) %}. The company pays a rate of interest on the debt {% r_D %} so that the debt at time
{% T %} is
{% D(T) = e^{r_DT}D(0) %}
- Corporate Assets The company also begins with assets that are contributed by the company's investors. The value of the assets at any time is given by a function {% A(t) %}.
- Corporate Equity At time {% T %}, the company is liquidated and the debt holders are paid off, if any money is left over, it goes to the equity holders. That is to say, if the {% A(T) \leq D(T) %}, then the debt holders receive the value of the assets. If {% A(T) > D(T) %}, then the debt holders receive {% D(T) %} and the equity holders receive {% A(T) - D(T) %}. This means that the equity holders own a call option that matures at time T with strike price {% A(T) - D(T) %}.