Good evening everyone, I would like to ask a question about Monte Carlo and PDE Pricing. For an American option, which one should we use, Monte Carlo method or PDE method? The same question for an Asian option such as an Asian call? As far as I know, PDE method have a downside which is the curse of dimensionality. However, I wonder whether this should be the main reason why Monte Carlo method is the favorite one? Thanks in advance!
For American (or any HJB problem), numerical methods are depending on the dimensionality.
Below dimension 3 (even 4), a PDE will do the job nicely, whereas above, MC methods are more appropriate.
There are many factors to consider. But mainly, in my opinion, you may choose the method depending on the complexity of the option and the resources you have. PDE method is usually used to solve problem whose complexity level is similar to problems you may solve using trees, and that using other approaches is not suitable.
In the other hand, using Monte Carlo allows you to consider any property you may think when creating an option, as long as you can model it.