Analytical Solutions of a Continuous Arithmetic Asian Model for Option Pricing using Projected Differential Transform Method

摘要

In financial mathematics, the procedure forfinding the solutions of the Black-Scholes model defined interms of Arithmetic Asian Option (AAO) is one of the mosttasking issues when considering its corresponding analyticalsolutions. In this paper, such analytical solution of a continuousarithmetic Asian option is obtained through the application of aproposed semi-analytical approach known as ProjectedDifferential transform Method (PDTM). The Asian optionmodel in continuous arithmetic form witnesses the applicationof PDTM for the first time in literature (to the authors’ best ofknowledge). The PDTM entails less computational work, evenwithout neglecting the high level of accuracy. The obtainedsolution is in agreement with those in literature via othersolution methods. In terms of recommendation, the proposedsolution method will be of great interest for related versions orforms of Asian option pricing models (geometric) likewise otherfinancial nonlinear differential models.