References
Amadi, I. U., Azor, P. A. and Chims, B. E. (2020). Crank-Nicolson Analysis of Black- Scholes Partial Differential Equation for Stock Market Prices. Academia Arena.12(1):1-22. Amadi, I.U., Osu. B.O. and Davies, I.(2022). A Solution to Linear Black-Scholes Second order Parabolic Eqaution in Sobolev Spaces. International journal of Mathematics and Computer Research,10, issue 10,2938-2946. Amadi, I.U., Davies, I. Osu , B. O. and Essi, I.D. (2022).Weak Estimation of Asset Value Function of Boundary Value Problem Arising in Financial Market, Asian journal of Pure and Applied Mathematics, 4(3),600-615. Ankudinova, J. and M. Ehrhardt, (2008). On the numerical solution of nonlinear Black- Scholes equations. Comput Math. Applic:, 56:799-812. DO1: 10. 1016/j.camwa. 2008.02.005. arising in the pricing of contingent claims. Journal of financial and quantitative analysis. Black F, Scholes M. (1973). The Pricing of Options and Corporate Liabilities. The Journal of Political Economy. 81:637-654. Brennan, M. and Schwartz, E. (1978). Finite Difference Methods and Jump Processes arising in the pricing of contingent claims. Journal of financial and quantitative analysis. 5(4):461-474. Cerna, D., V. Pasheva, N. Popivanou and G. Venlcov, (2016). Numerical solution of the Black- Scholes equation. Using cubic spline wavelets proceedings of the AIP conference, (IPC’ 16), AIP Publishing, USA DO1: 10.1063/1. 4968447. Company, R., A. Gonzalez and L. Jodar, (2008). Numerical solution of modified Black- Scholes equation pricing stock options with discrete dividend. Math Comput. Modell., 44: 1058-1068. DO1: 10/1016/j.mcm. 2006.03.009. Cortes, J., L, Jodar, R. Sala and P. Sevilla-Peris, (2005). Exact and numerical solution of Black–Scholes matrix equation. Applied Math. Comput., 160: 607-613. DO1: 10. 1111/j. 1475-6803. 1996. tb00592. Diperna ,R.J and Lions, P.L. (1989) Ordinary Differential Equations, transport theory and Sobolev Spaces”. Invention maths. 98 ,511. Dremkova, E., and Ehrhardt, M. (2011). A high-order compact method for nonlinear Black– Scholes option pricing equations of American options. International Journal of Computer Mathematics, 88(13), 2782-2797. Fadugba,S.E and Nwozo, C.R (2013).Crank Nicolson Finite Difference Method for the valuation of options. The pacific journal of science and technology, 14,2 ,136-146. Fadugba, S. E. and Ayegbusi, F. D. (2020). Bilaterial Risky Partial Differential Equation Model for European Style Option. Journal of Applied Sciences. 20(3): 104-108. Fadugba, S. E., Chukwuma, N. and Teniola, B. (2012). The Comparative Study of Finite Difference Method and monte Carlo Method for Pricing European Option. Mathematical theory and Modelling. 2(2), 53-67. George ,K.K. and Kenneth ,K.L.(2019). Pricing a European Put Option by numerical methods. International journal of scientific research publications, 9,issue 11,2250- 3153. Heston.S.I. (1993). A closed form solution for options with stochastic volatility with application to bond and currency option, Rev. Financial Studies, 6 ,327. Hull, J. C. (2012). Option. Futures and other Derivatives. Pearson Education Inc ;7. Hull, J. C. (2013). Options. Futures and other Derivatives. (5.Ed) Edition: London Prentice Hall International. Macbeth, J. and Merville, L. (1979). An Empirical Examination of the Black-Scholes Call Option Pricing Model. Journal of Finance. 34(5):1173-1186. IJASMT E- ISSN 2489-009X , Nwobi, F. N, Annorizie, M. N. and Amadi, I. U. (2019). Crank- Nicolson Finite Difference Method in Valuation of Options. Communications in Mathematical Finance. 8(1):93- 122. B.O Osu. (2010).A stochastic model of the variation of the capital market price. International Journal of trade, Economics and Finance, 1, 297 Song, L. and W. Wang, (2013). Solution of the fractional difference Black – Scholes option pricing model by finite difference method. Abs Applied Anal., 2013: 1-11. 001:10. 155/2013/194286. Uddin, M. K. S., Siddiki,M.N.A.A and M. A. Hossain, (2015). Numerical solution of a linear Black – Scholes models: A comparative overview. Journal of Engineering. Razali H., (2006) The pricing efficiency of equity warrants: A Malaysian case. ICFAI journal of derivatives markets.3(3):6-22. Rinalini, K. P. (2006). Effectiveness of the Black-Scholes Model Pricing Options in Indian Option Market. The ICFAI Journal of Derivatives Markets. 6-19. Wokoma, D. S.A., Amadi, I. U. and Azor, P. A. (2020). Estimation of Stock Prices using Black Scholes Partial Differential Equation for Put Options. African Journal of Mathematics and Statistics Studies. 3(2): 80-89. Yueng .L.T.(2012).Crank-Nicolson scheme for Asian option. Msc thesis Department of Mathematical and actuarial Sciences, faculty of Engineering and Science. University of Tunku Abdul Rahman. 1-97. Zhang. H., F. Liu, I. Turner and S. Chen, (2016). The numerical simulation of the tempered fractional Black -Scholes equation for European double barrier option. Applied Math. Model; 40: 5819-5834.
