I am comparing two methods: Least squares by Longstaff and Schwartz and A Forward Monte Carlo method. I am not sure what price I should consider as the "true value" to compare these two approaches. Any suggestions are greatly appreciated. The option is an American call.
Given the optimal exercise boundary is only an estimate, both the methods underestimate the "true value" of the option.
A simple comparison would be whichever method produced higher price for the option is better.
For this comparison to make sense, you could
- re-use underlying stock simulation across both the methods.
- make sure variance of price produced is reasonably low for both.
The "better" value of the two is still a lower bound and doesn't really throw information on how big the error is.
You could implement dual method to produce upper bound and thus a range for the true option price.
Again, this range is meaningful only if the underlying stock simulation ( vol model ) is meaningful.
Remember 'garbage in garbage out'