MANZOOR AHMAD HAJAM

@mlritm.ac.in

ASSSTANT PROFESSOR, DEPARTMENT OF MATHEMATICS (H&S)
MARRI LAXMAN REDDY INSTITUTE OF TECHNOLOGY AND MANAGEMENT

MANZOOR AHMAD HAJAM


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https://researchid.co/mannu.butt28

EDUCATION

DOCTORATE IN MATHEMATICS

RESEARCH, TEACHING, or OTHER INTERESTS

Applied Mathematics, Modeling and Simulation, Computational Mathematics, Mathematics
6

Scopus Publications

Scopus Publications

  • Time Fractional Black–Scholes Model and Its Solution Through Sumudu Transform Iterative Method
    Manzoor Ahmad, Rajshree Mishra, Renu Jain
    Computational Economics, 2025
  • ANALYTICAL SOLUTION OF TIME FRACTIONAL BLACK-SCHOLES EQUATION WITH TWO ASSETS THROUGH NEW SUMUDU TRANSFORM ITERATIVE METHOD
    Manzoor Ahmad, Rajshree Mishra, Renu Jain
    Gulf Journal of Mathematics, 2023
    There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black-Scholes model on a single asset is a partial differential equation characterizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of the regular Black-Scholes model. Explicit solution of the problem has been obtained with the help of generalized Mittag-Leffer function. The numerical analysis prove that this method is efficacious in solving various problems of financial theory.
  • Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends
    Manzoor Ahmad, Raishree Mishra, Renu Jain
    Journal of Partial Differential Equations, 2023
  • Analytical solution of one dimensional time fractional Black-Scholes equation through Laplace adomian decomposition method
    Mathematics in Engineering Science and Aerospace, 2022
  • Solution of time–space fractional black–scholes european option pricing problem through fractional reduced differential transform method
    Manzoor Ahmad, Rajshree Mishra, Renu Jain
    Fractional Differential Calculus, 2021
    Mathematical model introduced by Black and Scholes express financial derivatives more significantly. This model with fractional derivatives resulting in fractional Black-Scholes (B-S) equation express financial problems in a better way. In this paper, we introduce the fractional reduced differential transform method (FRDTM) to solve the time-space fractional Black-Scholes equation executing European options. This method is a modified version of the original differential transform method (DTM). This method proves to be valid for solving time-space Black-Scholes equation as it reduces the computational work to a greater extent. Moreover, this method helps in finding the solution without linearization or discretization. The efficiency of the method is tested by solving certain examples. The proposed mathematical representation can be useful to understand and solve time-space fractional differential equations arising in financial mathematics and other related fields.
  • A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation
    MANZOOR AHMAD, RAJSHREE MISHRA, RENU JAIN
    Creative Mathematics and Informatics, 2021
    In this paper, fractional reduced differential transform method (FRDTM) is operated to solve time fractional Black-Scholes American option pricing equation paying no dividends.The Black-Scholes model plays a significant role in the evaluation of European or American call and put options. The advantage of the proposed method to other existing methods is that it finds the solution without discretization or transformation. While using this method, no recommended assumptions are needed and hence the computational work reduces to a greater extent. Numerical experiments prove that the proposed method is efficient and valid for obtaining the solution of time fractional Black-Scholes equation governing American options. This method proves to be powerful for solving general fractional order partial differential equations (PDEs) existing in the field of Science, Engineering and other related fields.