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




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1

Department of Mathematics, Covenant University, Canaanland, Otta, 112103, Nigeria

2

Department of Mathematics, University of Ibadan, Ibadan, 200213, Nigeria





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Academic Editor: Carlo Cafaro

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





Author: Sunday O. Edeki 1,* , Olabisi O. Ugbebor 1,2 and Enahoro A. Owoloko 1

Source: http://mdpi.com/



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