Please enter verification code
Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation
Mathematics Letters
Volume 2, Issue 2, April 2016, Pages: 19-24
Received: Jul. 7, 2016; Accepted: Jul. 27, 2016; Published: Oct. 11, 2016
Views 2941      Downloads 101
Bright O. Osu, Department of Mathematics, College of Physical and Applied Sciencs, Michael Okpara University of Agriculture, Umudike, Nigeria
Joy Ijeoma Adindu-Dick, Department of Mathematics, Faculty of Physical and Biological Sciences, Imo State University, Owerri, Imo State, Nigeria
Article Tools
Follow on us
Assessing the stock price indices is the foundation of forecasting the market risk. In this paper, we derived a seemingly Black-Scholes parabolic equation. We then solved this equation under given conditions for the optimal prediction of the expected value of assets.
Fractal Scaling Exponent, Black-Scholes Equation, Assets Price Return, Optimal Value, Parabolic Equation
To cite this article
Bright O. Osu, Joy Ijeoma Adindu-Dick, Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation, Mathematics Letters. Vol. 2, No. 2, 2016, pp. 19-24. doi: 10.11648/
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Aydogan, K., & Booth, G. G. (1988). Are there long cycles in common stock returns? Southern Economic Journal, 55, 141-149.
Black, F., & Karasinski, P. (1991). Bond and options pricing with short rate and lognormal. Financial Analysis Journal, 47 (4), 52-59.
Black, F., & Scholes, M. (1973). The valuation of options and corporate liabilities. Journal of Econometrics, 81, 637-654.
Cheung, Y. W., Lai, K. S., & Lai, M. (1994). Are there long cycles in foreign stock returns? Journal of International Financial Markets, Institutions and Money, 3 (1), 33-48.
Cutland, N., Kopp, P., & Willinger, W. (1995). Stock price returns and the Joseph effect: A fractal version of the Black-Scholes model. Progress in Probability, 36, 327-351.
Fang, H., Lai, K., & Lai, M. (1994). Fractal structure in currency futures price dynamics. The Journal of Futures Markets, 14, 169-181.
Greene, M. T., & Fielitz B. D. (1997). Long term dependence in common stock returns. Journal of Financial Economics, 5, 339-349.
Hurst, H. E., (1951). Long term storage capacity of reservoir. Transactions of the American Society of Civil Engineers, 116, 770-799.
Lo, A. W., (1991). Long term memory in stock market prices. Econometrica, 59, 1279-1313.
Mandelbrot, B. B., (1982). The fractal geometry of nature. New York: Freeman.
Mandelbrot, B. B., (1997). Fractals and scaling in finance:Discontinuity, Concentration, Risk. New York: Springer-Verlag.
Mandelbrot, B. B., & Wallis, J. R. (1969). Robustness of the rescaled range in the measurement of non-cyclic long-run statistical dependence. Water Resources Research, 5, 967-988.
Muzy, J., Delour, J., & Bacry, E., (2000). Modelling fluctuations of financial time series: from cascade process to stochastic volatility Model. Euro. Phys. Journal B, 17, 537-548.
Shiryaev, A. N., (1999). Essentials of stochastic finance. Singapore: World Scientific.
Teverovsky, V., Taqqu, M., & Willinger, W., (1999). A critical look at Lo’s modified R/S statistic. Journal of statistical planning and inference, 80, 211-227.
Tokinaga, S., Moriyasu, H., Miyazaki, A, & Shimazu, N. (1997). Forecasting of time series with fractal geometry by using scale transformations and parameter estimations obtained by the wavelet transform. Electronics and Communications in Japan, 80 (3), 8-17.
Wallis, J. R., & Matalas, N. C., (1970). Small sample properties of H and K-estimators of the Hurst coefficient. Water Resources Research, 6, 1583-1594.
Willinger, W., Taqqu, M., & Teverovsky, V., (1999). Stock market prices and long-range dependence. Finance and Stochastic, 3, 1-13.
Xiong, Z., (2002). Estimating the fractal dimension of financial time Series by wavelets systems. Engineering-Theory and Practice, 12, 48-53.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186