There’s something I really can’t crack since a couple days ago and I was wondering if you could help me with this.

I read in a finance dissertation the following:

“Assume a bull call spread composed of two European call options with respective strike prices K_{1} and K_{2}, and maturities T_{1} and T_{2}, where K_{1} < K_{2} and 1 is held as a long position, while 2 is held as a short position. If we compose the same bull spread with American options, the value of the new portfolio is strictly larger than the first portfolio.”

To me the above would make sense, since the American options allow eventually to close the trade sooner in case of a particularly good payoff. On the other hand, this seems to disagree with another theorem, stating that because American options on non-dividend paying stocks are never exercised early then they are equivalent to European call options.

Is anyone able to provide any insight into this?