Closed-Form Solution of European Option under Fractional Vasicek Model

  • Seham Al. Roweathi Mathematics Department, College of Science, Jouf University, Sakaka, Saudi Arabia
  • Mohamed Kharrat Mathematics Department, College of Science, Jouf University, Sakaka, Saudi Arabia
Keywords: Fractional Vasicek model, European option, Stochastic Interest Rate, Adomian Decomposition


This paper specifically deals with how the powerful tools of fractional calculus are applied to compute European option prices under the Fractional Vasicek Model.


Adomian, G. Nonlinear stochastic operator equations. Academic Press, New York, 1986.

Benchohra, M., Graef, J.R. and Mostefai, F.-Z. Weak Solutions for Boundary-Value Problems with

Nonlinear Fractional Differential Inclusions. Nonlinear Dynamics and Systems Theory 11 (3) (2011)


Black, F. and Scholes, M.S. The pricing of options and corporate liabilities. The Journal of Political

Economy 81 (1973) 637-654.

Bohner, M. and Zheng, Y. On analytical solution of the Black-Scholes equation. Appl. Math. Lett. 22(2009) 309-313.

Company, R., Navarro, E., Pintos, J.R. and Ponsoda, E. Numerical solution of linear and nonlinear

Black-Scholes option pricing equations. Comput. Math. Appl. 56 (2008) 813-821.

Cox, J.C., Ingersoll, J.E. and Ross, S.A. A Theory of the Term Structure of Interest Rates. Econometrica53 (1985) 385-407.

Daftardar-Gejji, V. and Bhalekar, S. Solving multiterm linear and nonlinear diffusion wave equations of fractional order by Adomian decomposition method. Appl. Math. Comput202 (2008) 113-120.

Daftardar-Gejji, V. and Jafari, H. Adomian decomposition: a tool for solving a system of fractinal

differential equations. J.Math. Anal. Appl301 (2005) 508-518.

Fallahgoul, H.A., Focardi, S.M. and Fabozzi, F.J. Fractional Calculus and Fractional Processes with Applications to Financial Economics. Elsevier, September 2016.

Ghandehari, M.A.M. and Ranjbar, M. European Option Pricing of Fractional Version of the Black Scholes Model: Approach Via Expansion in Series. International Journal of Nonlinear Science 17 (2)(2014) 105-110.

Heston,S L. Closed form solution for options with stochastic volatility with application to bonds and currency options. Rev Financ Stud 6 (1993) 327-343.

Hull, J.C. Options, futures, and other derivatives. Prentice Hall, Upper Saddle River, 1997.

Hull, J. and White, A. The Pricing of Options on Assets with Stochastic Volatilities. The Journal of Finance 42 (1987) 281-300.

Kharrat M., Closed-Form Solution of European Option under Fractional Heston Model, Nonlinear Dynamics and Systems Theory. (2018);18(2):191-195.

Kharrat, M. Pricing American put Option under Fractional Heston Model. Pramana J.Phys. 95, , 3 (2021).

Kharrat, M., Pricing American put Option under Fractional Model. Filomat.(2021): 35 (10).

Kumar, S., Yildirim, A., Khan, Y., Jafari, H., Sayevand, K. and Wei, L. Analytical Solution of Fractional Black-Scholes European Option Pricing Equation by Using Laplace Transform. Journal of Fractional Calculus and Applications 2 (8) (2012) 1-9.

Podlubny, I. Fractional Differential Equations Calculus. Academic Press, New York, 1999.

Vasicek, O. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5(2),(1977) 177-188.

Xiaozhong, Y., LifeiEmail, W., Shuzhen, S. and Xue, Z. A universal difference method for time-space fractional Black-Scholes equation. 2016; . Advances in Difference Equations DOI: 10.1186/s13662-016-0792-8 (2016).

Yu, J.M., Luo, Y.W., Zhou, S.B. and Lin, X.R. Existence and Uniqueness for Nonlinear Multi-variables Fractional Differential Equations. Nonlinear Dynamics and Systems Theory 11 (2) (2011) 213-221.

Zhang, H., Liub, F., Turner, I. and Yang, Q. Numerical solution of the time fractional

Black-Scholes model governing European options. Computers and Mathematics with Applications (2016)