A Remark on Gatheral's 'Most-Likely Path Approximation' of Implied Volatility

4 Pages Posted: 3 Nov 2009

See all articles by Martin Keller-Ressel

Martin Keller-Ressel

Dresden University of Technology - Department of Mathematics

Josef Teichmann

ETH Zurich; Swiss Finance Institute

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

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

Martin Keller-Ressel (Contact Author)

Dresden University of Technology - Department of Mathematics ( email )

Zellescher Weg 12-14
Willers-Bau C 112
Dresden, 01062
Germany

Josef Teichmann

ETH Zurich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

HOME PAGE: http://www.math.ethz.ch/~jteichma

Swiss Finance Institute ( email )

c/o University of Geneva
40 Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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