MC vs. Finite Difference Methods

[sak]

The previous post had a great link. What about this one. I know in a limiting case FD and Trinomial trees are the same. When and why should we use FD or MC over the other?

Also I have read in Joshi's book where it says MC is difficult to use when pricing American options (early exercise feature). Well if there is no dividend it would not be exercised until expiration, so why should MC be difficult for such straight forward situation? OR even if there was a early exercise, IF-Then-ELSE can be used in each simulation for MC.

Any discussion is appreciated.

 

[Eugene Krel]

Monte Carlo methods in finance - Wikipedia, the free encyclopedia

 

[Daniel Duffy]

"I know in a limiting case FD and Trinomial trees are the same"

Yes and no, kind of.

The trinomial corresponds loosely to an explicit FDM but it originates from different principles.

http://www.wilmott.com/messageview.cfm?catid=34&threadid=75580&FTVAR_MSGDBTABLE=

FDM is fast, predictable, accurate and good for the greeks.