Barrier Shifts for Hedging Barrier Options

Summary

The document asks whether a trader should shift the effective barrier when hedging barrier options, focusing on up-and-out calls and down-and-in puts. The question contrasts knock-out and knock-in behavior: a hedge in an out option may be unwound when the barrier is crossed, while an in option can require a rapid change in delta exposure around activation. It raises the concern that the need for a barrier shift may differ across these payoff types.

The answer argues that barrier shifting is needed when hedging the options it identifies, because delta hedging near the barrier can encounter very large gamma. Moving the hedge barrier is presented as a way to keep the hedge from triggering at the contractual barrier. However, the response is brief and does not derive the adjustment, quantify its size, or address how it depends on market conditions, model assumptions, or the trader’s hedging objective. It therefore offers a qualitative explanation rather than a complete pricing or risk-management procedure.

Key ideas

• Barrier options can have very large gamma near their barrier.
• The answer recommends shifting the hedge barrier for the option types it names.
• The proposed shift is intended to keep the hedge from hitting the contractual barrier.
• The discussion gives no formula or guidance for selecting the size of the shift.

Tags

# Barrier Shifts - necessary for up-and-out call / down-and-in put?


# Barrier Shifts - necessary for up-and-out call / down-and-in put?












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.

## Answer by william lee (score 2)

https://quant.stackexchange.com/a/54799

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.