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I know it has nice properties relating to Roger Lee's moment formula and the Heston model asymptotics, but I am just curious how Jim Gatheral came up with this formula in the first place. I read a post somewhere saying the motivation for JG was that he might want to have a linear slope for the put wing and a square root of a quadratic for the call wing. But this doesn't make much sense and rigor to me. Can someone advise?

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  • $\begingroup$ There were other IV interpolation formulas before. I remember using one called the Salomon Smile Model which was based on work by Gross and Waltner in 1995. The formulas were very ad hoc and tried to fit the observed curve with some mathematical expression pulled out of a hat. Eventually Gatheral came up with a "second generation" formula that had some desirable properties (as you mention) and displaced the earlier approaches. It was a trial and error process AFAIK. Gatheral put the final brick in the wall. $\endgroup$
    – nbbo2
    Oct 1 at 7:45

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