Let's consider an incomplete market where I am pricing a complex derivative (Say a Bermudan). I hedge vega by a vanilla option(S). Let's say at t=1 I want to re-hedge. However, I have no guarantee that the price of my vanilla option is sufficient to be able to re-hedge. Indeed, self financing requires that, I need the same amount of the vanilla option as I needed before, which is likely not to be the case.

Is this reasoning correct? If yes, how do we justify vega hedging a complex derivative? Is there a hack/robustness to why this works?


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