ALTERNATIVE APPROACH FOR SOLVING A EUROPEAN POWER PUT OPTION MODEL WITH MODIFIED-LOG-POWER PAYOFF FUNCTION

Abstract

The main goal of this paper is to propose an alternative approach based on the celebrated transform of Mellin type (MT) for solving a European Power Put Option Model (EPPOM) in the sense of Modified-Log-Power Payoff Function (MLPPF) under the geometric Brownian motion. The MT has the capability of tackling complex functions by means of its fundamental properties and it is closely related to other well-known transforms such as Laplace and Fourier types. Using the MT inversion formula, convolution property and final time condition, the fundamental valuation formula of EPPOM was obtained. Moreover, the proposed MLPPF was also compared with other existing payoff functions. Also, the prices of EPPO generated by means of MT were compared with that of the celebrated Black-Scholes model. Hence, it is assumed that the underlying asset price pays no dividend yield.