  Mathematically, the execution of an American-style financial derivative is
commonly reduced to solving an optimal stopping problem. Breaking the general
assumption that the knowledge of the holder is restricted to the price history
of the underlying asset, we allow for the disclosure of future information
about the terminal price of the asset by modeling it as a Brownian bridge. This
model may be used under special market conditions, in particular we focus on
what in the literature is known as the "pinning effect", that is, when the
price of the asset approaches the strike price of a highly-traded option close
to its expiration date. Our main mathematical contribution is in characterizing
the solution to the optimal stopping problem when the gain function includes
the discount factor. We show how to numerically compute the solution and we
analyze the effect of the volatility estimation on the strategy by computing
the confidence curves around the optimal stopping boundary. Finally, we compare
our method with the optimal exercise time based on a geometric Brownian motion
by using real data exhibiting pinning.
