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I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method.

How do I obtain the early exercise boundary within the same LSM framework?

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For a vanilla option, this is a very slow way to get the boundary, and it's somewhat unreliable for any option.

In either a more standard grid scheme or in a LS solver, you obtain the boundary by finding two nodes such that one of them has option value equal to early exercise value, and its neighbor has option value above early exercise value.

This gives you an interval of underlying prices between which the boundary must lie. To narrow down that interval, you must increase the number of points in your grid.

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