An efficient approach for integer and non-integer barrier options model in a Caputo sense

Abstract

This paper proposes an efficient approach for solving Fractional Barrier Option Model (FBOM). The approach of the Caputo Fractional Reduced Differential Transform Method (CFRDTM) which is the combination of the Caputo Fractional Derivative (CFD) and the Reduced Differential Transform Method (RDTM) is employed. The emphasis is laid on CFD which is more suitable for the study of differential equations of fractional order. It is assumed that the stock price pays no dividend and follows a marked point process. Based on CFRDTM, a series solution for FBOM has been obtained successfully. The valuation formula for the price of Barrier Option (BO) with fractional order is also obtained. Moreover, the approximate solution obtained via CFRDTM is expressed in the form of a convergent series with computed components. An illustrative example is presented to measure the performance of CFRDTM in terms of accuracy, efficiency and suitability. The results obtained via CFRDTM were compared with the other existing methods such as the Laplace Adomian Decomposition Method (LADM), Two Dimensional Differential Transform Method (TDDTM) and the Analytical Value (AV). Hence, CFRDTM is found to be accurate, efficient and a suitable approach for obtaining an approximate solution of FBOM.