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A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

Author

Listed:
  • Elisa Alòs
  • Jorge A. León
  • Monique Pontier
  • Josep Vives

Abstract

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

Suggested Citation

  • Elisa Alòs & Jorge A. León & Monique Pontier & Josep Vives, 2008. "A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility," International Journal of Stochastic Analysis, Hindawi, vol. 2008, pages 1-17, February.
    • Handle: RePEc:hin:jnijsa:359142
    DOI: 10.1155/2008/359142
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    Cited by:

    1. Hossein Jafari & Ghazaleh Rahimi, 2019. "Small-Time Asymptotics In Geometric Asian Options For A Stochastic Volatility Jump-Diffusion Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-19, March.
    2. Bernardo D'Auria & Jos'e A. Salmer'on, 2021. "Anticipative information in a Brownian-Poissonmarket: the binary information," Papers 2111.01529, arXiv.org.
    3. R. Merino & J. Pospíšil & T. Sobotka & J. Vives, 2018. "Decomposition Formula For Jump Diffusion Models," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-36, December.
    4. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Josep Vives, 2019. "Decomposition formula for jump diffusion models," Papers 1906.06930, arXiv.org.
    5. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2021. "Anticipative information in a Brownian-Poisson market: the binary information," DES - Working Papers. Statistics and Econometrics. WS 33624, Universidad Carlos III de Madrid. Departamento de Estadística.

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