THE NORMALIZING TRANSFORMATION OF THE IMPLIED VOLATILITY SMILE
Нормализующая трансформация кривой подразумеваемой волатильности
2011-06-05
SCID: 54.1/jm7a3ads
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Black–Scholes implied volatilityEuropean payoff pricing formulasimplied volatility skew no-arbitrage boundsimplied volatility smilenormalizing transformation
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Abstract (AI)
We study specific nonlinear transformations of the Black–Scholes 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.
Key Findings
1
Pricing formulas for European payoffs are expressed directly in terms of the implied volatility smile.
2
Specific nonlinear transformations of Black–Scholes implied volatility reveal remarkable properties of the volatility surface.
3
The paper derives no-arbitrage bounds on the implied volatility skew.
Research Object
Black–Scholes implied volatility smile (volatility surface)
Research Subject
Nonlinear normalizing transformations of the implied volatility and their implications: properties of the volatility surface, no-arbitrage bounds on the implied volatility skew, and pricing formulas for European payoffs expressed via the implied volatility smile
Publication Details
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2011-06-05
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