A remark on Gatheral's 'most-likely path approximation' of implied volatility
AbstractWe give a rigorous proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we fix the problem of a circular definition in the original derivation of Gatheral, who introduced this implied volatility representation in his book 'The Volatility Surface'.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0911.0562.
Date of creation: Nov 2009
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-11-07 (All new papers)
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