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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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    1. Robert Savit, 1989. "Nonlinearities and chaotic effects in options prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 9(6), pages 507-518, December.
    2. Savit, R., 1989. "Nonlinearities And Chaotic Effects In Options Prices," Papers 184, Columbia - Center for Futures Markets.
    3. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-337, July.
    4. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Steven C. Blank, 1991. "“Chaos” in futures markets? A nonlinear dynamical analysis," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 11(6), pages 711-728, December.
    7. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
    8. Chou, Ray Yeutien, 1988. "Volatility Persistence and Stock Valuations: Some Empirical Evidence Using Garch," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 279-294, October-D.
    9. Gregory P. Decoster & Walter C. Labys & Douglas W. Mitchell, 1992. "Evidence of chaos in commodity futures prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(3), pages 291-305, June.
    10. Amin, Kaushik I & Ng, Victor K, 1993. "Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
    11. Hinich, Melvin J & Patterson, Douglas M, 1985. "Evidence of Nonlinearity in Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(1), pages 69-77, January.
    12. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    13. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    14. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
    15. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    16. Bailey, Warren & Stulz, René M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(1), pages 1-12, March.
    17. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    18. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-368, July.
    19. Murray Frank & Thanasis Stengos, 1989. "Measuring the Strangeness of Gold and Silver Rates of Return," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 553-567.
    20. Harvey, Campbell R & Whaley, Robert E, 1991. "S&P 100 Index Option Volatility," Journal of Finance, American Finance Association, vol. 46(4), pages 1251-1261, September.
    21. Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(1), pages 31-56, March.
    22. repec:bla:jfinan:v:44:y:1989:i:4:p:1011-23 is not listed on IDEAS
    23. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
    24. Campbell R. Harvey & Robert E. Whaley, 1992. "Dividends and S&P 100 index option valuation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(2), pages 123-137, April.
    25. Sheikh, Aamir M., 1991. "Transaction Data Tests of S&P 100 Call Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(4), pages 459-475, December.
    26. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    27. Whaley, Robert E., 1981. "On the valuation of American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 9(2), pages 207-211, June.
    28. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 71-90, July.
    29. Akgiray, Vedat, 1989. "Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts," The Journal of Business, University of Chicago Press, vol. 62(1), pages 55-80, January.
    30. Roll, Richard, 1984. "A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-1139, September.
    31. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    32. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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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. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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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