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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. 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.
    3. 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.
    4. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. 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.
    6. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.
    7. 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.
    8. 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.

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