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Given that an American option can be exercised at any time, how does one handle algorithmically shorting an American option in a back test? I am not sure what the best practice is to simulate the early exercise for selling American Options in a backtest.

There are two approaches I can think of:

  1. Assume that the option gets exercised if it crosses an arbitrary percent in the money.
  2. Treat the option the same way you would handle a European option.
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An American Call without dividends is never exercised before maturity, because it is always better to sell it instead. With dividends, one would exercise if the value of future dividends is higher than the time value (from selling the Call).

An American put without dividends is exercised when $S$ hits an optimal exercise boundary (e.g. if $S=0$ one would always exercise because the maximum payoff is reached). Finding the optimal exercise boundary for an AM put is however still an open question, some researches assume an explicit functional and fit it to the model.

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