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On the second derivative of the at-the-money implied volatility in stochastic volatility models

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Abstract

In this paper we compute analytically the at-the-money second derivative of the implied volatility curve as a function of the strike price, for correlated stochastic volatility models. We obtain an expression for the short-time limit of this second derivative in terms of the first and second Malliavin derivatives of the volatility process and the correlation parameter.

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  • Elisa Alòs & Jorge A. León, 2014. "On the second derivative of the at-the-money implied volatility in stochastic volatility models," Economics Working Papers 1458, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2016.
    • Handle: RePEc:upf:upfgen:1458
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    1. Elisa Alòs & Yan Yang, 2014. "A closed-form option pricing approximation formula for a fractional Heston model," Economics Working Papers 1446, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    3. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
    4. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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