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Smiling under stochastic volatility

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  • Rubio Irigoyen, Gonzalo
  • León, Angel
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    Abstract

    This paper studies the behavior of the implied volatility function (smile) when the true distribution of the underlying asset is consistent with the stochastic volatility model proposed by Heston (1993). The main result of the paper is to extend previous results applicable to the smile as a whole to alternative degrees of moneyness. The conditions under which the implied volatility function changes whenever there is a change in the parameters associated with Hestons stochastic volatility model for a given degree of moneyness are given.

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    File URL: https://addi.ehu.es/bitstream/10810/6755/1/wp2002-02.pdf
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    Bibliographic Info

    Paper provided by University of the Basque Country - Department of Foundations of Economic Analysis II in its series DFAEII Working Papers with number 2002-02.

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    Date of creation: Sep 2003
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    Handle: RePEc:ehu:dfaeii:200202

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    Postal: Dpto. de Fundamentos del Análisis Económico II, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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    Related research

    Keywords: volatility smile; stochastic volatility; skewness; kurtosis; option pricing;

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    References

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    1. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    3. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 211-239, June.
    4. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    5. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
    6. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
    7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    8. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    9. Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
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