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I'm trying to come up with the implied volatility skew adjusted delta for SPY options. I'm working with the following formula:
Skew Adjusted Delta = Black Scholes Delta + Vega * Vol Skew Slope.
I fitted a cubic polynomial to the volatility data, but I am not sure at which points to measure the slope.
Judging by the math in a paper by Vahamaa (1999), you should measure the slope using the options closest to the strike you are examining. In other words, suppose that you are trying to come up with the skew-adjusted delta of an SPY option with strike of 130. Then the skew slope should be based on the 129 and 131 strike options. If these points happen to be very illiquid, then you can, in principle, estimate the slope based on options further away from the strike of interest, but the skew adjustment is a local adjustment, and so the relevant slope is the slope at that strike.
