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Deterministic versus stochastic volatility: implications for option pricing models


  • Paul Brockman
  • Mustafa Chowdhury


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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    References listed on IDEAS

    1. Ram, Rati & Spencer, David E, 1983. "Stock Returns, Real Activity, Inflation, and Money: Comment," American Economic Review, American Economic Association, vol. 73(3), pages 463-470, June.
    2. Liu, Y Angela & Hsueh, L Paul & Clayton, Ronnie J, 1993. "A Re-examination of the Proxy Hypothesis," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 16(3), pages 261-268, Fall.
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    4. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
    5. Bodie, Zvi, 1976. "Common Stocks as a Hedge against Inflation," Journal of Finance, American Finance Association, vol. 31(2), pages 459-470, May.
    6. Geske, Robert & Roll, Richard, 1983. " The Fiscal and Monetary Linkage between Stock Returns and Inflation," Journal of Finance, American Finance Association, vol. 38(1), pages 1-33, March.
    7. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    8. Asprem, Mads, 1989. "Stock prices, asset portfolios and macroeconomic variables in ten European countries," Journal of Banking & Finance, Elsevier, vol. 13(4-5), pages 589-612, September.
    9. Y. Angela Liu & L. Paul Hsueh & Ronnie J. Clayton, 1993. "A Re-Examination Of The Proxy Hypothesis," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 16(3), pages 261-268, September.
    10. Fama, Eugene F, 1982. "Inflation, Output, and Money," The Journal of Business, University of Chicago Press, vol. 55(2), pages 201-231, April.
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    Cited by:

    1. Kyrtsou, Catherine & Vorlow, Costas, 2009. "Modelling non-linear comovements between time series," Journal of Macroeconomics, Elsevier, vol. 31(1), pages 200-211, March.
    2. Sergii Kuchuk-Iatsenko & Yuliya Mishura, 2016. "Option pricing in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Simulation," Papers 1601.01128,
    3. 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.

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