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What are some valid techniques that can be used to simulate how changes in the underlying are most likely to impact implied volatility along with the skew of all strikes for options with the same expiration. I am interested in both equity index and commodities.

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Hi, welcome to quant.SE! Thank you for asking your question here. Do I understand correctly that you're interested in the volatility surface? – Bob Jansen Jul 29 '14 at 6:23
I'm interested in understanding how implied volatility evolves from a day to day change in the underlying. For example if underlying were to move -3% in one day IV for all strikes with same expiration could rise but the original ATM strike would than be offset by the skew since it was further from ATM. I'm trying to determine how my Greeks evolve from underlying changes but I also realize that constant volatility is not realistic in all scenarios. – user3803295 Jul 29 '14 at 12:51
I believe SABR might give me what I am looking for. The question is whether or not is this overkill and are there alternatives. Also how does one incorporate sticky delta, sticky strike, etc... into this. – user3803295 Jul 29 '14 at 13:27

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