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Bayesian Analysis of the Black-Scholes Option Price

  • Darsinos, T.
  • Satchell, S.E.

This paper investigates the statistical properties of the Black-Scholes option price under a Bayesian approach. We incorporate randomness, both in the price process and in volatility, to derive the prior and posterior densities of a European call option. Expressions for the density of the option price conditional on the sample estimates of volatility and on the asset price respectively, are also derived. Numerical results are presented to compare how the dispersion of the option price changes in the transition from prior to posterior information, where information may be price or sample variance or both.

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File URL: http://www.econ.cam.ac.uk/research/repec/cam/pdf/wp0102.pdf
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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0102.

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Length: 37
Date of creation: Jan 2001
Date of revision:
Handle: RePEc:cam:camdae:0102
Note: EM
Contact details of provider: Web page: http://www.econ.cam.ac.uk/index.htm

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  8. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
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  11. Morgan, I G, 1976. "Stock Prices and Heteroscedasticity," The Journal of Business, University of Chicago Press, vol. 49(4), pages 496-508, October.
  12. Arrow, Kenneth J & Fisher, Anthony C, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," The Quarterly Journal of Economics, MIT Press, vol. 88(2), pages 312-19, May.
  13. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  14. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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  17. 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.
  18. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  19. 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(06), pages 791-807, December.
  20. Dixit, A., 1988. "Entry And Exit Decisions Under Uncertainty," Papers 91, Princeton, Department of Economics - Financial Research Center.
  21. 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.
  22. Day, Theodore E. & Lewis, Craig M., 1988. "The behavior of the volatility implicit in the prices of stock index options," Journal of Financial Economics, Elsevier, vol. 22(1), pages 103-122, October.
  23. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  24. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  25. Karolyi, G. Andrew, 1993. "A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 579-594, December.
  26. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
  27. Hwang, S. & Satchell, S. E., 1998. "Implied Volatility Forecasting: A Comparison of Different Procedures," Accounting and Finance Discussion Papers 98-af38, Faculty of Economics, University of Cambridge.
  28. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  29. 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.
  30. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  31. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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