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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. 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.
    2. 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).
    3. 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.
    4. van Garderen, Kees Jan, 2001. "Optimal prediction in loglinear models," Journal of Econometrics, Elsevier, vol. 104(1), pages 119-140, August.
    5. 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.
    6. 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.
    7. 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.

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