Abstract
In this chapter, we first introduce normal distribution, lognormal distribution, and their relationship. Then we discuss multivariate normal and lognormal distributions. Finally, we apply both normal and lognormal distributions to derive Black-Scholes formula under the assumption that the rate of stock price follows a lognormal distribution.
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Notes
- 1.
See Cox et al. (1979), “Option pricing: a simplified approach” for details.
- 2.
Values of X = $90, S = $92. 5, r = 0. 0435 were obtained from Section C of the Wall Street Journal on December 2, 1991. And σ = 0. 2194 is estimated in terms of monthly rate of return during the period January 1989 to November 1991.
- 3.
See Cheng F. Lee et al. (1990), Security Analysis and Portfolio Management (Glenview, I11: Scott, Foresman/Little, Brown), 754–760.
References
Anderson, T. W. 1984. An introduction to multivariate statistical analysis, 2nd Edition, Wiley, New York.
Cox, J. C. and S. A. Ross. 1976. “A Survey of Some New Results in Financial Option Pricing Theory”. The Journal of Finance, 31(2), 383–402.
Cox, J. C., S. A. Ross, and M. Rubinstein. 1979. “Option pricing: a simplified approach.” Journal of Financial Economics 7, 229–263.
Johnson, N. L. and S. Kotz. 1970. Continuous univariate distributions – I Distributions in statistics, Wiley, New York.
Johnson, N. L. and S. Kotz. 1972. Distributions in statistics: continuous multivariate distribution, Wiley, New York.
Lee, C. F. et al. 1990. Security analysis and portfolio management, Scott, Foresman/Little, Brown, Glenview, I11.
Rubinstein, M. 1976. “The Valuation of Uncertain Income Streams and the Pricing of Options”. The Bell Journal of Economics, 7(2), 407–425.
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Lee, C.F., Lee, J.C., Lee, A.C. (2010). Normal, Lognormal Distribution and Option Pricing Model. In: Lee, CF., Lee, A.C., Lee, J. (eds) Handbook of Quantitative Finance and Risk Management. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77117-5_27
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DOI: https://doi.org/10.1007/978-0-387-77117-5_27
Publisher Name: Springer, Boston, MA
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