# How to hedge a perpetual barrier option?

I have encountered the following question during my interview: How to have a static hedging of a perpetual barrier up-and-out call option in practice? Strike K = 110, barrier B = 120 for example?

MY

• The real answer to this is to chuck it in the portfolio you already have and hedge the risk you end up with.
– will
Mar 9, 2019 at 21:24
• @will Interviewer asked me to hedge with only stock, he didn't ask for an exact hedging, just an approximation.
– Fred
Mar 10, 2019 at 10:17
• If you can only hedge with the stock, then you would do the same. Look at the risk of the trade and dynamically hedge the delta it goves you.
– will
Mar 10, 2019 at 22:06
• That looks like a CBBC en.wikipedia.org/wiki/Callable_bull/bear_contract Mar 12, 2019 at 1:55

Note that the maximum option payoff is 10, and is attained at $$S=120$$. If you buy $$10/120 = 0.0833...$$ worth of stock for each option sold, then at any point in time, your portfolio will be worth at least the payoff. That is your static hedge. It’s very expensive vs the “true” price of the option, but that’s what your static hedge is.