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Deterministic versus stochastic volatility: implications for option pricing models

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  • Paul Brockman
  • Mustafa Chowdhury

Abstract

The Black-Scholes (1973) option pricing model (BSOPM) rests on the assumption that the variance of stock returns is deterministic. However, if stock return volatility is a stochastic process, then the present form of commonly used option pricing models is misspecified and arbitrage-based arguments are invalid. The purpose of this paper is to investigate whether implied stock return volatility is deterministic (with non-linear dependencies) or stochastic. Correlation dimensions are computed using the method of Grassberger and Procaccia (1983) and simple bootstrapping techniques are applied in order to distinguish stochastic from deterministic systems. Results reported herein add support to the growing literature on preference-based stochastic volatility models and generally reject the notion of deterministic volatility.

Suggested Citation

  • Paul Brockman & Mustafa Chowdhury, 1997. "Deterministic versus stochastic volatility: implications for option pricing models," Applied Financial Economics, Taylor & Francis Journals, vol. 7(5), pages 499-505.
    • Handle: RePEc:taf:apfiec:v:7:y:1997:i:5:p:499-505
    DOI: 10.1080/096031097333367
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    Cited by:

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    2. Zouhaier Dhifaoui, 2022. "Determinism and Non-linear Behaviour of Log-return and Conditional Volatility: Empirical Analysis for 26 Stock Markets," South Asian Journal of Macroeconomics and Public Finance, , vol. 11(1), pages 69-94, June.
    3. Sergii Kuchuk-Iatsenko & Yuliya Mishura, 2016. "Option pricing in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Simulation," Papers 1601.01128, arXiv.org.
    4. Charlotte S. Hansen & Bjorn E. Tuypens, 2007. "Spanning tests for options using principal components methods," Applied Financial Economics, Taylor & Francis Journals, vol. 17(9), pages 739-746.
    5. Vipul Kumar Singh, 2015. "Conjoint Analysis of Option and Volatility Models," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 14(3), pages 258-289, December.
    6. Hong, Hui & Bian, Zhicun & Chen, Naiwei, 2020. "Leverage effect on stochastic volatility for option pricing in Hong Kong: A simulation and empirical study," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    7. Maria C Mariani & Md Al Masum Bhuiyan & Osei K Tweneboah & Hector Gonzalez-Huizar & Ionut Florescu, 2019. "Volatility Models Applied to Geophysics and High Frequency Financial Market Data," Papers 1901.09145, arXiv.org.
    8. Dai, Min & Tang, Ling & Yue, Xingye, 2016. "Calibration of stochastic volatility models: A Tikhonov regularization approach," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 66-81.
    9. Mariani, Maria C. & Bhuiyan, Md Al Masum & Tweneboah, Osei K. & Gonzalez-Huizar, Hector & Florescu, Ionut, 2018. "Volatility models applied to geophysics and high frequency financial market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 304-321.

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