WOLFRAM|DEMONSTRATIONS PROJECT

Robustness of the Longstaff-Schwartz LSM Method of Pricing American Derivatives

​
monomial base
Laguerre base
Chebyshev base
scaled
initial stock price
40
strike price
40
volatility
0.1
risk-free interest rate
0.06
continuous dividend
0.03
time to expiry
1
number of paths
30
50
100
degree
2
new sample
binomial tree: 1.15202
Longstaff–Schwartz: 1.15322
This Demonstration shows the Longstaff–Schwartz least squares Monte Carlo method of computing the value of an American put option. We approximate the American option by a Bermudan option with 50 exercise times. The key point of the method is the estimation of conditional expectations by least squares regression on data obtained from Monte Carlo simulation using a basis for the space of
L
2
-functions. In this Demonstration we use three different kinds of bases. We show the graphs of the functions that estimate conditional expectations at the exercise points on a graph, below the value of the option computed by means of the Longstaff–Schwartz method, and the value computed by means of the binomial tree method with 1000 time steps.