New answers tagged volatility-smile
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Apparently Hagan et al original formula has a problem, and strictly speaking is incorrect. This was later corrected by Obloj 2008 using the BBF paper giving the implied volatilities directly from the Dupire PDE:
https://arxiv.org/pdf/0708.0998.pdf
I did not check your claims against the original paper but it is a possibility that you have precisely bumped ...
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