Merton
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)
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) %}
Assets
The company also begins with assets that are contributed by the companys investors. The value of the assets at any time is
given by a funtion {% A(t) %}.
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) %}.
