The Normalizing Transformation of the Implied Volatility Smile

10 Pages Posted: 23 Aug 2012

Date Written: October 2012

Abstract

We study specific nonlinear transformations of the BlackÔÇôScholes implied volatility to show remarkable properties of the volatility surface. No arbitrage bounds on the implied volatility skew are given. Pricing formulas for European payoffs are given in terms of the implied volatility smile.

Keywords: implied volatility, no arbitrage bounds, variance swap, gamma swap

Suggested Citation

Fukasawa, Masaaki, The Normalizing Transformation of the Implied Volatility Smile (October 2012). Mathematical Finance, Vol. 22, Issue 4, pp. 753-762, 2012. Available at SSRN: https://ssrn.com/abstract=2134703 or http://dx.doi.org/10.1111/j.1467-9965.2011.00483.x

Masaaki Fukasawa (Contact Author)

Osaka University

1-1 Yamadaoka
Suita
Osaka, 565-0871
Japan

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