Currently I am reading Basic Black Scholes: Option Pricing and Trading by Timothy Falcon Crack.
At page $42,$ the author mentions the following.
If an option position includes short American-style options, then the payoff-diagram may be misleading. That is because you can be “assigned an exercise” on the short option, and then you never reach expiration. Similarly, if an option position includes options of different maturity, then final pay-off is an odd concept; and in this case, the plot is not necessarily composed of straight lines with kinks.
I totally fail to grasp the meaning of above sentences.
What is the author trying to deliver?