I want to ask, what is the meaning of this symbol in red circle?
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1It is a "one" meaning "Characteristic function" (or "indicator function) of the set placed as the index : 1 on this set, 0 outside; sometimes the alternative 1/0 is meant as true/false. – Jean Marie Aug 22 '20 at 16:20
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1It's standard notation for the characteristic function. In your case, for, say, the up-and-in option, it is $1$ if the asset price ever got to $B$ or greater and it is $0$ otherwise. – lulu Aug 22 '20 at 16:21
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This function is a characteristic or an indicator function. Exact description of this function you can find e.g. here https://en.wikipedia.org/wiki/Indicator_function.
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