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A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics

Author

Listed:
  • Alexey MEDVEDEV

    (HEC-University of Geneva and FAME)

  • Olivier SCAILLET

    (HEC Genève and FAME, Université de Genève)

Abstract

In this paper we propose a simple non-parametric calibration procedure of option prices based on the short term asymptotics of implied volatilities. The approximation formula is derived for a general one factor jump-diffusion specification nesting most of the theoretical models typically used for option pricing. Using sets of reasonable parameter values we show that the procedure is capable of producing accurate estimates of key model functional relationships. Its implementation on a set of S&P500 option price data yields two major empirical results. First, the square root process for the variance is not consistent with the data. Second, Poisson jumps in returns do not help explaining the skew of short term implied volatilities.

Suggested Citation

  • Alexey MEDVEDEV & Olivier SCAILLET, 2004. "A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics," FAME Research Paper Series rp93, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp93
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Thomas Mazzoni, 2018. "Asymptotic Expansion of Risk-Neutral Pricing Density," IJFS, MDPI, vol. 6(1), pages 1-26, March.
    2. Elisa Alòs & Jorge A. León & Josep Vives, 2006. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Economics Working Papers 968, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Cheng-Few Lee & Oleg Sokolinskiy, 2015. "R-2GAM stochastic volatility model: flexibility and calibration," Review of Quantitative Finance and Accounting, Springer, vol. 45(3), pages 463-483, October.
    4. S. De Marco & C. Martini, 2012. "The Term Structure Of Implied Volatility In Symmetric Models With Applications To Heston," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-27.

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    More about this item

    Keywords

    Option pricing; stochastic volatility; asymptotic approximation; jump-diffusion;
    All these keywords.

    JEL classification:

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

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