Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T14:01:28.817Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  11 February 2009

John L Knight  and
Stephen E. Satchell
John L Knight
Affiliation:
University of Western Ontario
Stephen E. Satchell
Affiliation:
Trinity College, and University of Cambridge
Get access Rights & Permissions [Opens in a new window]

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.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 6 , December 1997 , pp. 791 - 807
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I. A. (1964) Handbook of Mathematical Functions. Applied Mathematics Series 55. National Bureau of Standards. Washington, DC: Dover Publications.Google Scholar
Arrow, K.J. & Fisher, A.C. (1974) Environmental preservation uncertainty, and irreversibility. Quarterly Journal of Economics 88, 312–319.CrossRefGoogle Scholar
Bar-Lev, J. & Enis, P. (1988) Sign-preserving unbiased estimators in linear exponential families. Journal of the American Statistical Association, 1187–1189.CrossRefGoogle Scholar
Brenner, M. & Subrahmanyam, M. (1988) A simple formula to compute the implied standard deviation. Financial Analysts Journal, September, 80–83.CrossRefGoogle Scholar
Butler, J.S. & Schachter, B. (1986) Unbiased estimation of the Black/Schoels formula. Journal of Financial Economics 15, 341–357.CrossRefGoogle Scholar
Dixit, A. (1989) Entry and exit decisions under marketing. Journal of Political Economy 97 (3), 621–638.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and Its Applications, vol. II. New York: Wiley.Google Scholar
Hull, J.C. (1993) Options, Futures and Other Derivative Securities, 2nd ed.Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar
Hull, J.C. & White, A. (1987) The pricing of options on assets with stochastic volatilities. Journal of Finance 42, 281–300.CrossRefGoogle Scholar
Kemp, M.H.D. (1996) Actuaries and Derivatives. Paper prepared for the Institute of Actuaries, London, 28 October.Google Scholar
Lehmann, E.L. (1983) Theory of Point Estimation. New York: Wiley.CrossRefGoogle Scholar
Lo, A. (1986) Statistical tests of contingent claims asset-pricing models: A new methodology. Journal of Financial Economics 17, 143–174.CrossRefGoogle Scholar
MacShahe, F.J. (1947) Integration. Princeton, New Jersey: Princeton University Press.Google Scholar
McDonald, R. & Siege, D.) (1985) Investment and the valuation of firms when there is an option to shut down. International Economic Review 26, 331–349.CrossRefGoogle Scholar
McDonald, R. & Siegel, D. (1986) The value of waiting to invest. Quarterly Journal of Economics 106, 707–727.CrossRefGoogle Scholar
Pyle, D.H. (1995) U.S. savings and loan crisis. In Jarrow, R.A., Maksimowe, V., & Ziemba, W.T. (eds.), Handbook in Operations Research and Management Science, vol. 19: Finance. Amsterdam: North-Holland.Google Scholar
Widder, D.V. (1946) Laplace Transform. Princeton, New Jersey: Princeton University Press.Google Scholar