Confidence Interval for Solutions of the Black-Scholes Model

Document Type: Research Paper

Authors

1 Department of Financial Sciences, Kharazmi University, Tehran, Iran

2 Department of Economics, Kharazmi University, Tehran, Iran

10.22034/amfa.2019.1869742.1231

Abstract

The forecast is very complex in financial markets. The reasons for this are the fluctuation of financial data, Such as Stock index data over time. The determining a model for forecasting fluctuations, can play a significant role in investors deci-sion making in financial markets. In the present paper, the Black Scholes model in the prediction of stock on year later value, on using data from mellat Bank and Ansar Bank shares in the year 2017-2018, in has been evaluated, and using a numerical method Euler Murayama and computer simulation with the Maple software, for simulated data, gained averages and Standard deviations, confidence interval and their normal histogram are plotted. Also, average of the answers obtained from computer simulations is compared with actual ones, and after ana-lyzing and reviewing the results, performance of the Black-Scholes model has been measured, in stock‌ value prediction. And in the end, this research is com-pared with internal article, and suggestions for future research are raised.

Keywords

Main Subjects


[1] Bjork, T., Arbitrage theory in continuous time, Oxford university press, 2009.

[2] Black, F., Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 1973, 81(3), P. 637-654.

[3] Cyganowski, S., Kloeden, P., Ombach, J., From Elementary Probability to Stochastic Differential Equations with MAPLE. Springer, 2001.

[4] Ehteshami, S., Hamidian, M., Hajiha, Z., Shokrollahi, S., Forecasting Stock Trend by Data Mining Algorithm, Advances in mathematical finance & applications, 2018, 3(1), P.97-105. Doi: 10.22034/A MFA.2018. 539138

[5] Gordon, M. J., The investment, financing, and valuation of the corporation. RD Irwin, 1962.

[6] Hull, J. C., Basu, S., Options, futures, and other derivatives, Pearson Education India, 2016.

[7] Hull, J., Treepongkaruna, S., Colwell, D., Heaney, R., Pitt, D., Fundamentals. Of futures and options markets. Pearson Higher Education AU, 2013.

[8] Klebaner, F. C., Introduction to stochastic calculus with applications.   World Scientific Publishing Company, 2005.

[9] Nasr, N., Farhadi Sartangi, M., Madahi, Z., A Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index, Advances in mathematical finance & applications, 2019, 4(1), P.15-30. Doi: :10.22034/AMFA.2019.583911.1172.

[10] Øksendal, B., Stochastic differential equations: An Introduction with Applications, Springer, 2003.

[11] Rezaei, N., Elmi, Z., Behavioural Finance Models and Behavioural Biases in Stock Price Forecasting, Advances in mathematical finance & applications, 2018, 3(4), P.67-82. Doi:10.22034/AMFA.2019.576127. 1118.

[12] Ross, S., Simulation, Academic Press, 2013.