1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Please describe the option: it is an American Call on how many assets? What is the underlying model GBM? $\endgroup$ – Alex C Apr 27 '17 at 1:01
  • $\begingroup$ hmm for an American call on a dividend paying stock, the American price is the same as the European. Unless the problem is high-dim use a tree or the BS formula. $\endgroup$ – Mark Joshi Apr 27 '17 at 4:37
  • $\begingroup$ *non-dividend paying stock. Indeed I would compare to the result obtained with a tree or finite difference scheme (if single or two assets). $\endgroup$ – Quantuple Apr 27 '17 at 7:54
  • $\begingroup$ Ok, so I can just use the standard Black-Scholes equation for a European option on a dividend paying stock? $\endgroup$ – Wolfy Apr 27 '17 at 17:39
  • 1
    $\begingroup$ the tree is much more accurate than MC methods for American options on a stock. Using the BS formula would be a very bad idea. $\endgroup$ – Mark Joshi Apr 28 '17 at 0:47
1
$\begingroup$

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'

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.