American option valuation: LSM method vs Binomial tree

[ChrisDerick]

Hello again guys,

For example, I would like to price an american option using simulation. The simplest method I would thought of is using the binomial tree with the value of option be max(exercise now, exercise later) at each node. Another interesting method would be Longstaff Schwartz's Least Squared MC method.

Would like to know the reason of applying least squared method (i.e. regression) to MC method; while I could've check for max(exercise now, exercise later) for each point, each path while I do MC?

Thanks.

 

[drahmah]

Monte Carlo was not thought to be possible for American options before Longstaff & Schwartz. This is because in American options, as you're running your simulation you need to constantly assess whether or not the benefit of immediate exercise exceeds the benefit of waiting. But if you wait, at each time step, you have to do another Monte Carlo again from the current stock price. So you cannot just continue running the same monte carlo simulation from t=0 to maturity. Like you said, Longstaff & Schwartz found a solution though doing regression based on the Brownian bridge concept.

I would think the binomial tree is simpler. You can do the put or call option with about 8 lines of C++ code.

 

[ChrisDerick]

Monte Carlo was not thought to be possible for American options before Longstaff & Schwartz. This is because in American options, as you're running your simulation you need to constantly assess whether or not the benefit of immediate exercise exceeds the benefit of waiting. But if you wait, at each time step, you have to do another Monte Carlo again from the current stock price. So you cannot just continue running the same monte carlo simulation from t=0 to maturity. Like you said, Longstaff & Schwartz found a solution though doing regression based on the Brownian bridge concept.

I would think the binomial tree is simpler. You can do the put or call option with about 8 lines of C++ code.

Ah. That does make sense. I guess Longstaff & Schwartz is the way to go if I am considering MC then...
Yeah I've built the Binomial tree. Thanks drahmah!

 

[Daniel Duffy]

others are

Quasi-exact
Finite element LCP problems
Several finite difference methods for speed and accuracy.

http://publications.nr.no/penaltyAmericanOptions.pdf