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I'm a clear on the differences between the two assumptions but a bit confused on the practical implementation.

1) The aim of choosing one of the two assumptions is to take into account the co-dynamic between the spot and the vol when delta hedging. As a result, it is similar to proxy vega hedge with spot. However, if we vega hedge, this proxy should be netted and as a result, delta hedge + vega hedge should be the same quantity independently from the initial assumption. Does that mean that we also need to modify the vega when choosing between one of the two assumptions?

2) I find a lot of information on how to modify the delta. Do we agree that we should also modify the gamma accordingly?

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