I am trying to find the implied volatility smile for an American call option with a known dividend during the option tenor. For the sake of argument, let's say today is Jan 1, the dividend $D$ is paid out in 30 days at time $T_1$, and the option expires in 60 days at time $T_2$. Since $r = 0$, $$D < K(1-e^{-r(T-T_1)}) = 0$$ isn't satisfied, so it may be optimal to exercise at $T_1$. In effect, we have a Bermudan option with possible exercise times $T_1$ and $T_2$. If I have price data for the option, how can I back out the implied volatility? Is there an additional simplification or approximation we can make since $r = 0$ that does better than Black's approximation?
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$\begingroup$ Bumping this $\qquad$ $\endgroup$– user369210Mar 17, 2018 at 5:00
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1$\begingroup$ Please don't bump $\endgroup$– Bob Jansen ♦Mar 17, 2018 at 9:03
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