To hedge/profit from a black swan move (index down 30%) jump, is there a way to quantify the strikes given the scenario above and VIX is trading >60, possibly at 100? I know that where delta = 25, that is the steepest part of the gamma and vega slope, peaking at ATM. Am I also right in saying this is where volga and speed is highest given the tangent line to the slope and concavity? If so, would buying a load of 1-5 puts vs 25 delta puts at the same dollar amount be a better P&L hedge/profit? I would like to see whether rate of change is higher for one vs other but I don't know what the IVs will be and how steep the skew gets when the move comes. Any way to extrapolate this? BTW, is there any retail software that will calculate 2nd and 3rd order derivatives and modify risk graphs for their inputs? Actually it doesn't have to be retail geared, price won't be a concern as a poor hedge will cost more. Search has yielded some results, but nothing conclusive.