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Abstract
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One of the modern financial theory’s biggest successes in terms of both approach and applicability has
been the Black-Scholes option pricing model. It is widely recognized that the value of an 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 an 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 resolving the
different equations for each step. In contrast to methods that have implicit solutions, the FPM yields a
closed form explicit solution.
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