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Stochastic Volatility Model with Time-dependent Skew

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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, December.
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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. Christian Bayer & Juho Happola & Ra'ul Tempone, 2017. "Implied Stopping Rules for American Basket Options from Markovian Projection," Papers 1705.00558, arXiv.org, revised Jun 2017.
    4. Dell'Era, Mario, 2010. "Geometrical Considerations on Heston's Market Model," MPRA Paper 21523, University Library of Munich, Germany.
    5. Dell'Era, Mario, 2010. "Vanilla Option Pricing on Stochastic Volatility market models," MPRA Paper 25645, University Library of Munich, Germany.
    6. A. Antonov & T. Misirpashaev, 2009. "Markovian Projection Onto A Displaced Diffusion: Generic Formulas With Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 507-522.
    7. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    8. A. M. Ferreiro & J. A. Garc'ia & J. G. L'opez-Salas & C. V'azquez, 2024. "SABR/LIBOR market models: pricing and calibration for some interest rate derivatives," Papers 2408.01470, arXiv.org.
    9. Dariusz Gatarek & Juliusz Jabłecki, 2021. "Between Scylla and Charybdis: The Bermudan Swaptions Pricing Odyssey," Mathematics, MDPI, vol. 9(2), pages 1-32, January.
    10. Simona Svoboda-Greenwood, 2009. "Displaced Diffusion as an Approximation of the Constant Elasticity of Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 269-286.
    11. Dell'Era, Mario, 2010. "Geometrical Approximation method and stochastic volatility market models," MPRA Paper 22568, University Library of Munich, Germany.

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