Abstract
We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of ‘forward implied variance’ in the original derivation of Gatheral, who introduced this representation in his book ‘The Volatility Surface’.
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References
Gatheral, J.: The Volatility Surface. Wiley Finance (2006)
Guyon, J., Henry-Labordère, P.: Nonlinear Option Pricing. CRC Press, Boca Raton (2013)
Lee, R.: Implied volatility: statics, dynamics, and probabilistic interpretation. Recent Advances in Applied Probability. Springer, New York (2004)
Acknowledgments
MKR acknowledges funding from the Excellence Initiative of the German Research Foundation (DFG).
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Keller-Ressel, M., Teichmann, J. (2015). A Remark on Gatheral’s ‘Most-Likely Path Approximation’ of Implied Volatility. In: Friz, P., Gatheral, J., Gulisashvili, A., Jacquier, A., Teichmann, J. (eds) Large Deviations and Asymptotic Methods in Finance. Springer Proceedings in Mathematics & Statistics, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-11605-1_8
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DOI: https://doi.org/10.1007/978-3-319-11605-1_8
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