Hedging Volatility

What volatility to use in the hedging procedure dictated by the BS model?

 

It may seem a stupid question at first, because it has already been answered by the IV. If you can price a particular option, meaning you have the IV available, it is straightforward solution to use this value as the volatility to hedge with. 

 

However, let assume you have a crystal ball and you know that the realized volatility is going to be 20%, but  you can negotiate your client into paying an IV of 25%. So you are selling the option more expensively that it is really worth. 

So which of the two values do I plug into the dynamic hedging strategy to hedge this sold option? 

As it turns out, it does not make that much of a difference anyway. This brings us to another strength of the BS model. It turns out that the model is so robust that almost any value will do. 

Most traders choose to use the IV for consistency reasons.  

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