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Let's say that I hold an American Call Option (ACO) and an European Call Option (ECO) in my portfolio on the same underlying, with same strike price and same maturity date. Given that I hold both options till the maturity date, will the return of my American Call Option have a lower volatility than the return time series of my European Call Option? It feels like since the price from the ACO is bounded from below with the ECO price, but wasn't able to prove it so far.

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    $\begingroup$ I don't know which vol is higher. But to compare the vols you have to compare the deltas of the ACO and ECO, not their prices. $\endgroup$
    – nbbo2
    Nov 19, 2021 at 10:33
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    $\begingroup$ The expected return (and thus the systematic risk) of an American put option is higher than the expected return of a European put option. The expected return (and thus the systematic risk) of an American call option is lower than the expected return of a European call option. $\endgroup$
    – Kevin
    Nov 19, 2021 at 10:58

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