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From The Implied Volatility Skew To A Robust Correction To Black-Scholes American Option Prices

Author

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  • JEAN-PIERRE FOUQUE

    (Department of Mathematics, North Carolina State University, Raleigh NC 27695-8205, USA)

  • GEORGE PAPANICOLAOU

    (Department of Mathematics, Stanford University, Stanford CA 94305, USA)

  • K. RONNIE SIRCAR

    (ORFE Department, Princeton University, Princeton, NJ 08544, USA)

Abstract

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of afixedboundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

Suggested Citation

  • Jean-Pierre Fouque & George Papanicolaou & K. Ronnie Sircar, 2001. "From The Implied Volatility Skew To A Robust Correction To Black-Scholes American Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 651-675.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:04:n:s0219024901001139
    DOI: 10.1142/S0219024901001139
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    Citations

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    Cited by:

    1. K. Maris & K. Nikolopoulos & K. Giannelos & V. Assimakopoulos, 2007. "Options trading driven by volatility directional accuracy," Applied Economics, Taylor & Francis Journals, vol. 39(2), pages 253-260.
    2. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.
    3. Elisa Al`os & Eulalia Nualart & Makar Pravosud, 2023. "On the implied volatility of European and Asian call options under the stochastic volatility Bachelier model," Papers 2308.15341, arXiv.org, revised Sep 2024.
    4. Vagnani, Gianluca, 2009. "The Black-Scholes model as a determinant of the implied volatility smile: A simulation study," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 103-118, October.
    5. Kyo Yamamoto & Akihiko Takahashi, 2009. "A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(4), pages 333-345, December.
    6. Max O. Souza & Jorge P. Zubelli, 2007. "On The Asymptotics Of Fast Mean-Reversion Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 817-835.
    7. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Shiva Chandra & Andrew Papanicolaou, 2019. "Singular Perturbation Expansion For Utility Maximization With Order-𝜖 Quadratic Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-18, November.

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