A remark on Gatheral's 'most-likely path approximation' of implied volatility

Details A remark on Gatheral's 'most-likely path approximation' of implied volatility A remark on Gatheral's 'most-likely path approximation' of implied volatility

2009-11-03

arxiv.org/abs/0911.0562v1

Economy

Quantitative Finance

Pricing of Securities

4 pages

Scientific paper

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 this implied volatility representation
in his book 'The Volatility Surface'.

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