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Recently I came across the topic of barrier shift for barrier/digital options. I found that most examples centred around down-and-in puts / up-and-in call / digitals.

I am wondering if we need barrier shift when pricing up-and-out call / down-and-in put? For example, if client buys up-and-out call and trader sells it, trader would have been buying delta to hedge the position. If the underlying goes beyond the barrier, the trader can sell the delta with profits, whereas for a up-and-in call/digital, trader has to suddenly buy a large amount of delta.

I am not sure about that. Please share your thoughts.

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  • $\begingroup$ The barrier shift is typically there to make risk managing it close to expiry easy - it will spread out the delta and lower the peak. $\endgroup$
    – will
    Commented Oct 7, 2018 at 8:46
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    $\begingroup$ Related question quant.stackexchange.com/questions/45841/… $\endgroup$
    – nbbo2
    Commented Jun 10, 2020 at 12:32

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Definelty barrier shift is necessary when hedging PDI and CUI, thats because you always want to hedge your barrier as it was no hitted because you would experience enormous gamma in that region. So you shift the barrier and in this way you will never hit the barrier in your hedge

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