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With 0% interest rates r-q is almost always < 0. Dividends are pretty much never continuous, so for an American option if the dividend you collect and interest you forgo collecting (or paying) being short the stock is larger than the value of the put (since when you punch a call you sell that call and buy 100 shares, thus selling the put). It's also worth ...


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The excercise should happen if the present value of the dividend yield minus risk free interest exceeds the value of the related put. As noted before this is only true if a position is deep in the money and volatility is low. On single stocks this decision is usually done right before dividend ex-date.


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I'm not sure that machine learning would lead to any practical solutions here. Do you really have enough data for that kind of techniques? I would suggest a different approach: assume that the exercise is optimal, but just based on a different cost function than the expected pay-off. If you can find a function that replicates well enough the past exercise ...


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Your question is too broad, but I there is plenty of examples of uses of machine learning to mimic human behaviour. For instance deep learning has been used 25 years ago to read checks in banks, or support vector machines 15 years ago to implement artificial vision, or bayesian networks to mimic expert diagnosis. I guess it would not be that hard to use ...


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I think that for any $q>0$ it becomes optimal to exercise an American call for a sufficiently high spot price $S$: if the spot increases enough, the dividend yield corresponds to sufficient cash dividend to render exercise optimal. This would happen irrespective of the value of $r$ or the sign of $r-q$. What matters is that, for a given strike $K$, the ...



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