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A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models

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  • Raúl Merino
  • Josep Vives

Abstract

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model, extending a previous decomposition formula for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used for this purpose are nonanticipative. In particular, we also see that equivalent results can be obtained by using Functional Itô Calculus. Using the same generalizing ideas, we also extend to nonexponential models the alternative call option price decomposition formula written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both the anticipative and the nonanticipative cases.

Suggested Citation

  • Raúl Merino & Josep Vives, 2015. "A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models," International Journal of Stochastic Analysis, Hindawi, vol. 2015, pages 1-11, June.
    • Handle: RePEc:hin:jnijsa:103647
    DOI: 10.1155/2015/103647
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    Cited by:

    1. El-Khatib, Youssef & Goutte, Stephane & Makumbe, Zororo S. & Vives, Josep, 2022. "Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset," Finance Research Letters, Elsevier, vol. 44(C).
    2. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Tommi Sottinen & Josep Vives, 2019. "Decomposition formula for rough Volterra stochastic volatility models," Papers 1906.07101, arXiv.org, revised Aug 2019.
    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. Takuji Arai, 2020. "Al\`os type decomposition formula for Barndorff-Nielsen and Shephard model," Papers 2005.07393, arXiv.org, revised Sep 2020.
    6. Youssef El-Khatib & Zororo S. Makumbe & Josep Vives, 2024. "Approximate option pricing under a two-factor Heston–Kou stochastic volatility model," Computational Management Science, Springer, vol. 21(1), pages 1-28, June.

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