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I have created some modifications of least squares monte carlo algorithm for pricing american options which gives me lower and upper bound. Now I want to test how good it works for options with highly nonlinear exercise boundaries.

Could you please suggest me what are these options? I think barrier options in high dimensions is one answer, but what are others?

I would be very grateful if you also linked some papers that studied how well particular methods worked on such options and maybe theoretical values of these options to compare with my results

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