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Great reads to further explore and better understand stochastic volatility models are the series of articles "Smile Dynamics" by Lorenzo Bergomi. As the name indicates the idea is to study stochastic volatility models not only as "smile models" (in the sense that SV models can be used to capture the state of the vanilla market by correctly accounting for ...


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It comes from Heat Kernel expansion and differential geometry. See Theorem 6 and Section 8 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1717676&download=yes



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