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Title

Optimization of the Black-Scholes Equation with the Numerical Method of Local Expansion to Minimize Risk Coverage

Year: 1400
COI: JR_AMFA-6-4_010
Language: EnglishView: 6
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Authors

Amirreza Keyghobadi - Department of Accounting,Economic and Accounting Faculty,Central Tehran Branch,Islamic Azad University, Tehran, Iran.
Shadan Behzadi - Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran.
Fatemeh Gervei - Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran

Abstract:

In this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The Black-Scholes equation is a partial differential equation, which describes the price of choice in terms of time and the collocation method is a method of deter-mining coefficients. Then we show the computational results and examine the performance of the method for the two options, the price of basic assets and its issues. These results show that the Jacoby method is more efficient in solving the Black Scholes equation, and the method error is less and the convergence rate is higher. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be solved by nonlinear solution methods, such as Newton's iterative method. The existence, uniqueness of the solution, and convergence of the methods are examined, and we will show in an example that by repeating then |u n+۱-u n |/|u n | <ε can be reached and this indicates the accuracy of the response to these methods.

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Paper COI Code

This Paper COI Code is JR_AMFA-6-4_010. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1275192/

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Keyghobadi, Amirreza and Behzadi, Shadan and Gervei, Fatemeh,1400,Optimization of the Black-Scholes Equation with the Numerical Method of Local Expansion to Minimize Risk Coverage,https://civilica.com/doc/1275192

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  • Behzadi, Sh.S., Yildirim, A., Application of Quintic B-Spline Collocation Method ...
  • Fey, R., & and Polte, U., Nonlinear Black-Scholes Equations in ...
  • Ksendal, B., Sulem, A., Maximum Principles for Optimal Control of ...
  • Ouafoudi, M. Gao, F., Exact Solution of Fractional Black-Scholes European ...
  • Slavova A., Kyurkchiev, N., Numerical Implementation of Generalizations of Black–Scholes ...
  • Sakthivel, K. Kim, J.H., Controllability and Hedgibility of Black-Scholes Equations ...
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    Type of center: Azad University
    Paper count: 14,218
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