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Fine-tune your smile: Correction to Hagan et al

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  • Jan Obloj

Abstract

In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term is consistent as $\beta\to 1$. Furthermore, numerical simulations show that it reduces or eliminates known pathologies of the earlier formula.

Suggested Citation

  • Jan Obloj, 2007. "Fine-tune your smile: Correction to Hagan et al," Papers 0708.0998, arXiv.org, revised Mar 2008.
    • Handle: RePEc:arx:papers:0708.0998
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    References listed on IDEAS

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    1. Patrick Hagan & Diana Woodward, 1999. "Equivalent Black volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 147-157.
    2. Fima Klebaner & Truc Le & Robert Liptser, 2006. "On Estimation of Volatility Surface and Prediction of Future Spot Volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 245-263.
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    Cited by:

    1. Jaegi Jeon & Kyunghyun Park & Jeonggyu Huh, 2021. "Extensive networks would eliminate the demand for pricing formulas," Papers 2101.09064, arXiv.org.
    2. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    3. Hyukjae Park, 2013. "Efficient valuation method for the SABR model," Papers 1308.0665, arXiv.org, revised Nov 2013.
    4. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.

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