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Mispricing in the Black-Scholes model: an exploratory analysis

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  • Sriplung, Kai-one

Abstract

The Black-Scholes option pricing model has been highly influential in security trading and in analyses of risk-price relationships, despite the fact that it has been shown to have an apparent unexplainable mispricing bias. This study examines the mispricing exhibited by the Black-Scholes model and shows that it can be explained by the estimation procedures utilized and the measures of volatility. Specifically, a model is constructed to test for the systematic over- or underpricing of the Black-Scholes model. Striking price and time-to-maturity are included in the model. The model also includes an autoregressive error structure. Recognizing the autocorrelation in the errors improves estimation efficiency and predictability of future option prices. The method of entering implied volatility into the model has a great impact. When only one estimated implied volatility was used to explain the option data, the Black-Scholes model exhibited a bias that was a similar function of striking price for all of the securities studied. When separate estimated implied volatilities for different option positions were used, the bias as a function of striking price and time-to-maturity varied among securities. Predictions of market option prices based on the model containing striking price, time-to-maturity, and an autoregressive error structure were more accurate than those based on the Black-Scholes model.

Suggested Citation

  • Sriplung, Kai-one, 1993. "Mispricing in the Black-Scholes model: an exploratory analysis," ISU General Staff Papers 1993010108000011187, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genstf:1993010108000011187
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    References listed on IDEAS

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    1. Bhattacharya, Mihir, 1980. "Empirical Properties of the Black-Scholes Formula Under Ideal Conditions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(5), pages 1081-1105, December.
    2. Chang, S J & Chen, Son-Nan, 1989. "A Study of Call Price Behavior under a Stationary Return Generating Process," The Financial Review, Eastern Finance Association, vol. 24(3), pages 335-354, August.
    3. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    4. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
    5. Choi, J. Y. & Shastri, Kuldeep, 1989. "Bid-ask spreads and volatility estimates : The implications for option pricing," Journal of Banking & Finance, Elsevier, vol. 13(2), pages 207-219, May.
    6. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    7. Chiras, Donald P. & Manaster, Steven, 1978. "The information content of option prices and a test of market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 213-234.
    8. Boyle, Phelim P. & Ananthanarayanan, A. L., 1977. "The impact of variance estimation in option valuation models," Journal of Financial Economics, Elsevier, vol. 5(3), pages 375-387, December.
    9. Butler, J. S. & Schachter, Barry, 1986. "Unbiased estimation of the Black/Scholes formula," Journal of Financial Economics, Elsevier, vol. 15(3), pages 341-357, March.
    10. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
    11. Barone-Adesi, Giovanni & Whaley, Robert E., 1986. "The valuation of American call options and the expected ex-dividend stock price decline," Journal of Financial Economics, Elsevier, vol. 17(1), pages 91-111, September.
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