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Showing 2 results for Ranjbar
Mojtaba Ranjbar, Somayeh Pourghanbar, Ebrahim Nasrabadi,
Volume 1, Issue 1 (6-2020)
Abstract
One of the greatest accomplishments in modern financial theory, in terms of both approach and applicability has been the BlackScholes option pricing model. It is widely recognized that the value of a European option can be obtained by solving the Black-Scholes equation. In this paper we use functional perturbation method (FPM) for solving Black-Scholes equation to price a European call option. The FPM is a tool based on considering the differential operator as a functional. The equation is expanded functionally by Frechet series. Then a number of successive partial differential equations (PDEs) are obtained that have constant coefficients and differ only in their right hand side part. Therefore we do not need to resolve the different equations for each step. In contrast to methods that have implicit solutions, the FPM yields a closed form explicit solution.
zahra Sarvari, Mojtaba Ranjbar, Shahram Rezapour,
Volume 2, Issue 1 (6-2021)
Abstract
In this paper, the polynomial differential quadrature method (PDQM) is implemented to find the numerical solution of the generalized Black-Scholes partial differential equation. The PDQM reduces the problem into a system of first order non-linear differential equations and then, the obtained system is solved by optimal four-stage, order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme. Numerical examples are given to illustrate the efficiency of the proposed method.
