A Remark on Gatheral's 'Most-Likely Path Approximation' of Implied Volatility
4 Pages Posted: 3 Nov 2009
Date Written: November 3, 2009
Abstract
We 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 the implied volatility representation in his book 'The Volatility Surface'.
Keywords: Implied Volatility, Local Volatility, Stochastic Volatility, Volatility Surface, most-likely path
Suggested Citation: Suggested Citation
Keller-Ressel, Martin and Teichmann, Josef, A Remark on Gatheral's 'Most-Likely Path Approximation' of Implied Volatility (November 3, 2009). Available at SSRN: https://ssrn.com/abstract=1499082 or http://dx.doi.org/10.2139/ssrn.1499082
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