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Stochastic Volatility Model with Time-dependent Skew

Author

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  • Vladimir Piterbarg

Abstract

A formula is derived for the 'effective' skew in a stochastic volatility model with a time-dependent local volatility function. The formula relates the total amount of skew generated by the model over a given time period to the time-dependent slope of the instantaneous local volatility function. A new 'effective' volatility approximation is also derived. The utility of the formulas is demonstrated by building a forward Libor model that can be calibrated to swaption smiles that vary across the swaption grid.

Suggested Citation

  • Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
  • Handle: RePEc:taf:apmtfi:v:12:y:2005:i:2:p:147-185
    DOI: 10.1080/1350486042000297225
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    References listed on IDEAS

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    1. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, June.
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    Cited by:

    1. Emmanuel Gobet & Ali Suleiman, 2013. "New approximations in local volatility models," Post-Print hal-00523369, HAL.
    2. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.
    3. Dell'Era, Mario, 2010. "Geometrical Considerations on Heston's Market Model," MPRA Paper 21523, University Library of Munich, Germany.
    4. Dell'Era, Mario, 2010. "Vanilla Option Pricing on Stochastic Volatility market models," MPRA Paper 25645, University Library of Munich, Germany.
    5. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    6. Dell'Era, Mario, 2010. "Geometrical Approximation method and stochastic volatility market models," MPRA Paper 22568, University Library of Munich, Germany.

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