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In financial mathematics, the procedure for finding the solutions of the Black-Scholes model defined in terms of Arithmetic Asian Option (AAO) is one of the most tasking issues when considering its corresponding analytical solutions. In this paper, such analytical solution of a continuous arithmetic Asian option is obtained through the application of a proposed semi-analytical approach known as Projected Differential transform Method (PDTM). The Asian option model in continuous arithmetic form witnesses the application of PDTM for the first time in literature (to the authors’ best of knowledge). The PDTM entails less computational work, even without neglecting the high level of accuracy. The obtained solution is in agreement with those in literature via other solution methods. In terms of recommendation, the proposed solution method will be of great interest for related versions or forms of Asian option pricing models (geometric) likewise other financial nonlinear differential models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]