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Market calibration under a long memory stochastic volatility model

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  • Jan Pospíšil
  • Tomáš Sobotka

Abstract

In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock.

Suggested Citation

  • Jan Pospíšil & Tomáš Sobotka, 2016. "Market calibration under a long memory stochastic volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 323-343, September.
    • Handle: RePEc:taf:apmtfi:v:23:y:2016:i:5:p:323-343
    DOI: 10.1080/1350486X.2017.1279977
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    Citations

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    Cited by:

    1. Jan Pospíšil & Tomáš Sobotka & Philipp Ziegler, 2019. "Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure," Empirical Economics, Springer, vol. 57(6), pages 1935-1958, December.
    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. Viktor Bezborodov & Luca Persio & Yuliya Mishura, 2019. "Option Pricing with Fractional Stochastic Volatility and Discontinuous Payoff Function of Polynomial Growth," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 331-366, March.
    6. Josef Danv{e}k & J. Posp'iv{s}il, 2020. "Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models," Papers 2006.13181, arXiv.org.
    7. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    8. Lahmiri, Salim & Bekiros, Stelios, 2020. "Nonlinear analysis of Casablanca Stock Exchange, Dow Jones and S&P500 industrial sectors with a comparison," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    9. Jan Posp'iv{s}il & Vladim'ir v{S}v'igler, 2019. "Isogeometric analysis in option pricing," Papers 1910.00258, arXiv.org.
    10. Jan Posp'iv{s}il & Tom'av{s} Sobotka & Philipp Ziegler, 2019. "Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure," Papers 1912.06709, arXiv.org.

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