American Option Prices and the Optimal Exercise Boundary

This demo computes American option prices and the corresponding optimal exercise boundary

In this demo, the price V of an American option is considered as a
function of the stock value S and time t, i.e. V = V(S,t). The financial
parameters like strike, volatility, etc. (a complete list is given below)
are assumed to be constants. The demo computes the option price for a
range of discrete stock values S(i) and a range of discrete time
values t(j).
The demo also computes the optimal exercise boundary Sf as a function
of time, i.e. Sf = Sf(t). For each discrete time value t(j), the value
Sf(j) is the last (in case of a put) or the first (in case of a call)
contact point with the payoff. This point gives the user the information
whether it is optimal to exercise the option at each discrete point in
time.

The results are visualized in three figures. The first figure is a graph
of the American option price at the initial time. For comparison reasons,
this figure also shows a graph of the corresponding European option
and a graph of the payoff. The second figure displays a surface of the
option price as a function of the stock value and time. Finally, the
third graph displays the optimal exercise boundary.

The demo is executed by running the scritp AmericanOptionDemo.m. This scritp calls the functions AmericanOption.m and FreeBoundary.m