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From implied to spot volatilities

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  • Valdo Durrleman

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Suggested Citation

  • Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
    • Handle: RePEc:spr:finsto:v:14:y:2010:i:2:p:157-177
    DOI: 10.1007/s00780-009-0112-1
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    References listed on IDEAS

    as
    1. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Valdo Durrleman & Nicole El Karoui, 2008. "Coupling smiles," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 573-590.
    4. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    5. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    6. Martin Schweizer & Johannes Wissel, 2008. "Arbitrage-free market models for option prices: the multi-strike case," Finance and Stochastics, Springer, vol. 12(4), pages 469-505, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Stefano Pagliarani & Andrea Pascucci, 2017. "The exact Taylor formula of the implied volatility," Finance and Stochastics, Springer, vol. 21(3), pages 661-718, July.
    2. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    3. Stefan Gerhold & I. Cetin Gulum & Arpad Pinter, 2013. "Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models," Papers 1310.3061, arXiv.org, revised May 2016.
    4. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    5. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    6. Peter K. Friz & Jim Gatheral, 2024. "Computing the SSR," Papers 2406.16131, arXiv.org.
    7. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    8. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    9. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Quantitative Finance, Taylor & Francis Journals, vol. 23(9), pages 1221-1258, September.
    10. Lingjiong Zhu, 2015. "Options with Extreme Strikes," Risks, MDPI, vol. 3(3), pages 1-16, July.
    11. Huy N. Chau & Duy Nguyen & Thai Nguyen, 2024. "On short-time behavior of implied volatility in a market model with indexes," Papers 2402.16509, arXiv.org, revised Mar 2025.
    12. Romain Bompis, 2017. "Weak approximations for arithmetic means of geometric Brownian motions and applications to Basket options," Working Papers hal-01502886, HAL.

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    More about this item

    Keywords

    Option price; Implied volatility; Spot volatility; Martingale representation; Asymptotic analysis; Itô–Wentzell formula; 60H10; 91B28; C60; G13;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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