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Calibration Of Stochastic Volatility Models Via Second-Order Approximation: The Heston Case

Author

Listed:
  • ELISA ALÒS

    (Departament d'Economia i Empresa, Universitat Pompeu Fabra and Barcelona Graduate School of Economics, c/Ramón Trias Fargas, 25–27, 08005 Barcelona, Spain)

  • RAFAEL DE SANTIAGO

    (Department of Managerial Decision Sciences, IESE Business School, Av. Pearson 21, 08034 Barcelona, Spain)

  • JOSEP VIVES

    (Departament de Probabilitat, Lògica i Estadística and Institut de Matemàtica de la Universitat de Barcelona (IMUB), Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain)

Abstract

In this paper, we present a new, simple and efficient calibration procedure that uses both the short and long-term behavior of the Heston model in a coherent fashion. Using a suitable Hull and White-type formula, we develop a methodology to obtain an approximation to the implied volatility. Using this approximation, we calibrate the full set of parameters of the Heston model. One of the reasons that makes our calibration for short times to maturity so accurate is that we take into account the term structure for large times to maturity: We may thus say that calibration is not "memoryless," in the sense that the option's behavior far away from maturity does influence calibration when the option gets close to expiration. Our results provide a way to perform a quick calibration of a closed-form approximation to vanilla option prices, which may then be used to price exotic derivatives. The methodology is simple, accurate, fast and it requires a minimal computational effort.

Suggested Citation

  • Elisa Alòs & Rafael De Santiago & Josep Vives, 2015. "Calibration Of Stochastic Volatility Models Via Second-Order Approximation: The Heston Case," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-31.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:06:n:s0219024915500363
    DOI: 10.1142/S0219024915500363
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Janek, Agnieszka & Kluge, Tino & Weron, Rafał & Wystup, Uwe, 2010. "FX smile in the Heston model," SFB 649 Discussion Papers 2010-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
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    Citations

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    Cited by:

    1. Takuji Arai, 2021. "Approximate option pricing formula for Barndorff-Nielsen and Shephard model," Papers 2104.10877, arXiv.org.
    2. Colin Turfus & Aurelio Romero-Berm'udez, 2023. "Analytic RFR Option Pricing with Smile and Skew," Papers 2301.01260, arXiv.org.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    8. Takuji Arai, 2020. "Al\`os type decomposition formula for Barndorff-Nielsen and Shephard model," Papers 2005.07393, arXiv.org, revised Sep 2020.
    9. 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.
    10. Siow Woon Jeng & Adem Kiliçman, 2021. "SPX Calibration of Option Approximations under Rough Heston Model," Mathematics, MDPI, vol. 9(21), pages 1-11, October.

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