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Entropy 2015, 17(11), 7510-7521; doi:10.3390/e17117510

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

1
Department of Mathematics, Covenant University, Canaanland, Otta, 112103, Nigeria
2
Department of Mathematics, University of Ibadan, Ibadan, 200213, Nigeria
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cafaro
Received: 31 May 2015 / Revised: 1 October 2015 / Accepted: 7 October 2015 / Published: 30 October 2015
(This article belongs to the Special Issue Dynamical Equations and Causal Structures from Observations)
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Abstract

In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algorithm can be followed for European put options. It is shown that PDTM is more efficient, reliable and better than the classical DTM and other semi-analytical methods since less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs) encountered in financial mathematics. View Full-Text
Keywords: analytical solution; Black–Scholes model; projected differential transform method; option valuation; European options; stochastic differential equations analytical solution; Black–Scholes model; projected differential transform method; option valuation; European options; stochastic differential equations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Edeki, S.O.; Ugbebor, O.O.; Owoloko, E.A. Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method. Entropy 2015, 17, 7510-7521.

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