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.
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$\begingroup$ Please describe the option: it is an American Call on how many assets? What is the underlying model GBM? $\endgroup$– Alex CCommented Apr 27, 2017 at 1:01
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$\begingroup$ 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 JoshiCommented Apr 27, 2017 at 4:37
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$\begingroup$ *non-dividend paying stock. Indeed I would compare to the result obtained with a tree or finite difference scheme (if single or two assets). $\endgroup$– QuantupleCommented Apr 27, 2017 at 7:54
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$\begingroup$ Ok, so I can just use the standard Black-Scholes equation for a European option on a dividend paying stock? $\endgroup$– WolfyCommented Apr 27, 2017 at 17:39
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2$\begingroup$ 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 JoshiCommented Apr 28, 2017 at 0:47
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1 Answer
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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'
