I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy.

Researching on the net and previous questions on this site imply that BS can be used, but input of the correct IV is the hard part. Tags like "the wrong number in the wrong formula to get the right price", "sticky delta vs sticky strike", "skew adjusted delta" and Derman's work are the solutions I have found so far.

Can anyone tell me if these are the latest or best methods, or is a stochastic vol model like SABR or Heston better? Is calculating one value for the position delta too optimistic - should the position delta actually be a range with associated confidence limits?


There's no best method. The question is : what is the behavior of the volatility structure (atm and skew) when the underlying moves? Each method assumes something different. In the real market, one method might work well for a period of time (in the sense that it minimizes residual p/l), but then another method might take over as best. Practitioners tend to experiment with different methods until they get comfortable which is best (as they see it). However, there's no accepted best method.

  • $\begingroup$ I agree. Best method I've come up with is to model the skew and calculate Greeks for a range of spot prices. Then tweak ATM vol and degree of skewness (rotate skew around spot) to see how T0 PnL will change under different vol conditions. Then calibrate the model daily. $\endgroup$ – Zeus Nov 25 '15 at 4:37
  • $\begingroup$ This question has generated a lot of views. For those looking at options modeling I suggest buying a copy of the following book which has helped me extensively with the math of options. espenhaug.com/books.html amazon.com/Complete-Guide-Option-Pricing-Formulas/dp/0071389970/… $\endgroup$ – Zeus Aug 16 '17 at 7:36

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