WOLFRAM|DEMONSTRATIONS PROJECT

Pricing American Options with the Two- and Three-Point Maximum Methods

​
time steps
15
time to expiry (years)
T
3
starting asset price
S
0
40
strike price
X
45
risk-free rate
r
0.07
dividend yield
δ
0
volatility
σ
0.3
This Demonstration shows the application of the "two-point maximum" and "three-point maximum" methods [2] in order to approximate the value of an American put. The Demonstration uses the trinomial method [3] and the fact that Bermudan options approximate American options to locate the optimal early exercise temporal points and estimate the values
P
2,max
and
P
3,max
. Use the controllers to set the time discretization for the trinomial tree and the American option parameters.
• The table shows the maximized
P
2,max
and
P
3,max
values of the Bermudan put options and their optimal early exercise temporal points, respectively. The table also displays the American put approximations after the application of Richardson extrapolation once and twice, respectively.
• The upper graph shows the value of a Bermudan option
P
2
, depending on the choice of its early exercise temporal point
t
1
. The red dot represents the optimal early exercise temporal point, which maximizes the value of the Bermudan option
P
2
.
• The lower 3D graph shows the value of a Bermudan option
P
3
, depending on the choice of its early exercise temporal points
t
1
and
t
2
. The red dot represents the optimal early exercise temporal points, which maximize the value of the Bermudan option
P
3
.