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We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms.
Handbook of Mathematical Functions
Abramowitz, M., & Stegun, I. 1964 · 1964
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The Volatility Smile and Its Implied Tree
Derman, E., & Kani, I. 1994 · 1994
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Arbitrage Bounds of the Implied Volatility Strike and Term Structures of European-Style Options
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Regimes of Volatility Some Observations on the Variation of S&P 500 Implied Volatilities
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Implied volatility functions: A reprise
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Ledoit, O., Santa-Clara, P., & Yan, S. 2002 · 2002
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A Common Principal Component Approach
Fengler, M., Härdle, W., & C.Villa. 2003 · 2003
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Implied Vol Constraints
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A parsimonious arbitrage-free implied volatility parameterization with applicationto the valuation of volatility derivatives
Gatheral, J. 2004 · 2004
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The Moment Formula for Implied Volatility at Extreme Strikes
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le Roux, M. 2007 · 2007
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