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Existence of Unbiased Estimators of the Black/Scholes Option Price, Other Derivatives, and Hedge Ratios

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  • Knight, John L
  • Satchell, Stephen E.

Abstract

In this paper, we reexamine the question of statistical bias in the classic Black/Scholes option price where randomness is due to the use of the historical variance. We show that the only unbiased estimated option is an at the money option.

Suggested Citation

  • Knight, John L & Satchell, Stephen E., 1997. "Existence of Unbiased Estimators of the Black/Scholes Option Price, Other Derivatives, and Hedge Ratios," Econometric Theory, Cambridge University Press, vol. 13(6), pages 791-807, December.
    • Handle: RePEc:cup:etheor:v:13:y:1997:i:06:p:791-807_00
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    Cited by:

    1. Darsinos, T. & Satchell, S.E., 2002. "The Implied Distribution for Stocks of Companies with Warrants and/or Executive Stock Options," Cambridge Working Papers in Economics 0217, Faculty of Economics, University of Cambridge.
    2. Peter C. B. Phillips & Jun Yu, 2009. "Simulation-Based Estimation of Contingent-Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
    3. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Analysis of the Black-Scholes Option Price," Cambridge Working Papers in Economics 0102, Faculty of Economics, University of Cambridge.
    4. Lin, Lisha & Li, Yaqiong & Gao, Rui & Wu, Jianhong, 2021. "The numerical simulation of Quanto option prices using Bayesian statistical methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. John Knight & Stephen Satchell, 2005. "A Re-Examination of Sharpe's Ratio for Log-Normal Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 87-100.
    6. Lisha Lin & Yaqiong Li & Rui Gao & Jianhong Wu, 2019. "The Numerical Simulation of Quanto Option Prices Using Bayesian Statistical Methods," Papers 1910.04075, arXiv.org.
    7. van Garderen, Kees Jan, 2001. "Optimal prediction in loglinear models," Journal of Econometrics, Elsevier, vol. 104(1), pages 119-140, August.

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