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Option pricing with quadratic volatility: a revisit

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  • Leif Andersen

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Suggested Citation

  • Leif Andersen, 2011. "Option pricing with quadratic volatility: a revisit," Finance and Stochastics, Springer, vol. 15(2), pages 191-219, June.
    • Handle: RePEc:spr:finsto:v:15:y:2011:i:2:p:191-219
    DOI: 10.1007/s00780-010-0142-8
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    References listed on IDEAS

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    1. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    2. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
    3. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    4. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    6. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    7. Christian Zuhlsdorff, 2001. "The pricing of derivatives on assets with quadratic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 235-262.
    8. Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Alexander Lipton & Andrey Gal & Andris Lasis, 2013. "Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new results," Papers 1312.5693, arXiv.org.
    2. Slobodan Milovanovi'c & Victor Shcherbakov, 2017. "Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methods," Papers 1711.09852, arXiv.org, revised Aug 2018.
    3. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    4. Paolo Guasoni & Miklós Rásonyi, 2015. "Fragility of arbitrage and bubbles in local martingale diffusion models," Finance and Stochastics, Springer, vol. 19(2), pages 215-231, April.
    5. Çetin, Umut & Larsen, Kasper, 2023. "Uniqueness in cauchy problems for diffusive real-valued strict local martingales," LSE Research Online Documents on Economics 118743, London School of Economics and Political Science, LSE Library.
    6. Craddock, Mark & Grasselli, Martino, 2020. "Lie symmetry methods for local volatility models," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3802-3841.
    7. Antoine Jacquier & Martin Keller-Ressel, 2015. "Implied volatility in strict local martingale models," Papers 1508.04351, arXiv.org.
    8. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    9. Peter Carr & Travis Fisher & Johannes Ruf, 2012. "Why are quadratic normal volatility models analytically tractable?," Papers 1202.6187, arXiv.org, revised Mar 2013.
    10. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    11. Stephen Taylor & Scott Glasgow & James Taylor & Jan Vecer, 2016. "Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 847-867, September.
    12. 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.
    13. Yukihiro Tsuzuki, 2024. "Boundary conditions at infinity for Black-Scholes equations," Papers 2401.05549, arXiv.org, revised Sep 2024.
    14. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    15. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2017. "Most-likely-path in Asian option pricing under local volatility models," Papers 1706.02408, arXiv.org, revised Aug 2018.
    16. Umut Cetin & Kasper Larsen, 2020. "Uniqueness in Cauchy problems for diffusive real-valued strict local martingales," Papers 2007.15041, arXiv.org, revised May 2022.
    17. Martin HERDEGEN & Martin SCHWEIZER, 2016. "Economically Consistent Valuations and Put-Call Parity," Swiss Finance Institute Research Paper Series 16-02, Swiss Finance Institute.
    18. Martin Herdegen & Martin Schweizer, 2018. "Semi‐efficient valuations and put‐call parity," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1061-1106, October.
    19. Mark Craddock & Martino Grasselli, 2016. "Lie Symmetry Methods for Local Volatility Models," Research Paper Series 377, Quantitative Finance Research Centre, University of Technology, Sydney.

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    More about this item

    Keywords

    Quadratic volatility; Strict local martingale; Put and call option pricing; Hitting time densities; Fourier series; Method of images; 91G20; 91G80; 60G40; 60G46; G12; G13;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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