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I am reading the section on Skew adjustment for binary options on wikipedia (https://en.wikipedia.org/wiki/Binary_option#Skew) and am trying to get my head around it and gain some intuition.

First question is regarding Binary Put options, following the same calculations as for the Binary call and constructing a put spread I get that the Skew adjustment in this case is instead + Vega of the vanilla put times the skew, meaning that the skew adjustment makes a binary put worth less (if Skew is negative). This also makes some sense intuitively as the Vega of the binary put is negative when SK, meaning that when prices drop (and volatility rises) we are gaining less (relatively speaking). Is this reasoning correct?

The second is about the magnitude of this adjustment, the Skew should be greater the further we are from ATM meaning the adjustment is larger, but the Vega of the vanilla should be decreasing as we get further from ATM so we have two competing effects. When is the skew adjustment necesarry to make, when is it neglibible? And are there more factors to consider than the moneyness of the option? On average, how large is the adjustment (in terms of % of the value of the non skew-adjusted option)?

Thank you

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  • $\begingroup$ Usually this dvol/dK adjustment is not done and market practitioners prefer pricing via tight spreads as explained here. $\endgroup$
    – AKdemy
    Commented Oct 29, 2021 at 23:13
  • $\begingroup$ @AKdemy Hi, ok that's interesting. Will the value of the call spread not by definition be exactly equal to that of the pricing with a dvol/dK adjustment if you let the spread approach zero? So is it instead standard to price it as a "realistic" call spread that would be used to hedge the digital, hence the preference for pricing with a put/call spread? If so, what is a realistic value of dK to use for pricing? $\endgroup$
    – Oscar
    Commented Oct 30, 2021 at 13:41
  • $\begingroup$ Simple pricers like Bloomberg's use a spread of 1% of strike, no matter the tenor, vol and underlying (for FX, equity is just BS unadjusted). More sophisticated pricers offer a flexible spread calculation. However, going close to zero is entirely unfeasible as your notional explodes for example. I recommend to read more than just a Wikipedia article. $\endgroup$
    – AKdemy
    Commented Oct 30, 2021 at 17:14
  • $\begingroup$ Thanks, the reason I'm looking into this is that I need to price a European barrier option (meaning it can be replicated, and priced, as a vanilla put and fixed number of binary puts). Do you think pricing the binary component as a put spread is more reasonable in this case? Do you have any references you could recommend? $\endgroup$
    – Oscar
    Commented Oct 30, 2021 at 18:32

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