Mathematics Letters

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Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation

Received: 07 July 2016    Accepted: 27 July 2016    Published: 11 October 2016
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Abstract

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.

DOI 10.11648/j.ml.20160202.11
Published in Mathematics Letters (Volume 2, Issue 2, April 2016)
Page(s) 19-24
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fractal Scaling Exponent, Black-Scholes Equation, Assets Price Return, Optimal Value, Parabolic Equation

References
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[2] Black, F., & Karasinski, P. (1991). Bond and options pricing with short rate and lognormal. Financial Analysis Journal, 47 (4), 52-59.
[3] Black, F., & Scholes, M. (1973). The valuation of options and corporate liabilities. Journal of Econometrics, 81, 637-654.
[4] 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.
[5] 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.
[6] Fang, H., Lai, K., & Lai, M. (1994). Fractal structure in currency futures price dynamics. The Journal of Futures Markets, 14, 169-181.
[7] Greene, M. T., & Fielitz B. D. (1997). Long term dependence in common stock returns. Journal of Financial Economics, 5, 339-349.
[8] Hurst, H. E., (1951). Long term storage capacity of reservoir. Transactions of the American Society of Civil Engineers, 116, 770-799.
[9] Lo, A. W., (1991). Long term memory in stock market prices. Econometrica, 59, 1279-1313.
[10] Mandelbrot, B. B., (1982). The fractal geometry of nature. New York: Freeman.
[11] Mandelbrot, B. B., (1997). Fractals and scaling in finance:Discontinuity, Concentration, Risk. New York: Springer-Verlag.
[12] 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.
[13] 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.
[14] Shiryaev, A. N., (1999). Essentials of stochastic finance. Singapore: World Scientific.
[15] 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.
[16] 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.
[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.
[18] Willinger, W., Taqqu, M., & Teverovsky, V., (1999). Stock market prices and long-range dependence. Finance and Stochastic, 3, 1-13.
[19] Xiong, Z., (2002). Estimating the fractal dimension of financial time Series by wavelets systems. Engineering-Theory and Practice, 12, 48-53.
Author Information
  • Department of Mathematics, College of Physical and Applied Sciencs, Michael Okpara University of Agriculture, Umudike, Nigeria

  • Department of Mathematics, Faculty of Physical and Biological Sciences, Imo State University, Owerri, Imo State, Nigeria

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  • APA Style

    Bright O. Osu, Joy Ijeoma Adindu-Dick. (2016). Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Mathematics Letters, 2(2), 19-24. https://doi.org/10.11648/j.ml.20160202.11

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    ACS Style

    Bright O. Osu; Joy Ijeoma Adindu-Dick. Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Math. Lett. 2016, 2(2), 19-24. doi: 10.11648/j.ml.20160202.11

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    AMA Style

    Bright O. Osu, Joy Ijeoma Adindu-Dick. Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Math Lett. 2016;2(2):19-24. doi: 10.11648/j.ml.20160202.11

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      title = {Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation},
      journal = {Mathematics Letters},
      volume = {2},
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      abstract = {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.},
     year = {2016}
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