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This study seems to be on point: http://christian-fries.de/finmath/foresightbias/Fries_ForesightBias.pdf


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One example could be someone using option strategies and its underlying dividends. In these cases, the trader could use early excersise to capture the dividend value. Google it for more information.


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The Black-Scholes PDE holds in the continuation region : $$ u_t = - \frac{1}{2} \sigma^2 u_{ss} $$ (ignoring interest rate). This says that theta is as smooth as gamma. The "smooth pasting" literature you mention shows that delta is continuous at the exercise boundary, but gamma has a jump. So theta has a jump as well. In other words, in the time ...


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american options are at least as expensive as their european counterparts. So it's enough to argue that european options increase in value as time to expiry prolongs, given other metrics remain the same. This is because of the "time value" of options. On the other hand, longer time give you more opportunity to early exercise, which adds in zero or positive ...


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For American options, the longer the maturity, the more choices for the optimal exercises time, then the option value is bigger. For example, consider maturities $T_1$ and $T_2$, for the same option except for different maturities. Any optimal exercise time within $[0, T_1]$ is a possible exercise time within $[0, T_2]$, with a better time possibly falls in ...



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