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In Monte Carlo pricing of American options we form two estimators:

  1. A high estimator that is biased upward because of "look-ahead" bias (i.e., at any given time we uses future information to decide whether to exercise).

  2. A low estimator that is biased downward because of using a suboptimal exercise policy.

I understand the upward bias of the high estimator, but why does it not also suffer from downward suboptimality bias? The implementation of the high estimator is based on backward induction which uses a suboptimal exercise policy.

Edit: I believe all the standard simulation methods to price American options (random trees, stochastic mesh, regression-based approaches) suffer from the above biases.

However, if it helps, I am specifically thinking about the random tree approach. It is the first approach described in Chapter 8 of the Monte Carlo book by Glasserman. The approach was initially presented in a 1997 paper by Broadie and Glasserman: called "Pricing American-style securities using simulation".

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    $\begingroup$ Hi, could you please add a reference or some (pseudo) code? There are multiple ways to value American options (even under MC). Thanks! $\endgroup$ Nov 12, 2021 at 5:25
  • $\begingroup$ My guess is that there is no suboptimality bias because the high estimator uses exercise policy that peeks into the future which is in fact better than any admissible exercise policy. In some sense the high bias can thus be viewed as the opposite of a suboptimality bias. $\endgroup$
    – arni
    Nov 12, 2021 at 6:44

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