Abstract & Overview
In this paper we explore the significance of maturity parameter when the Fourier method is applied in option pricing by using two different analytical solutions of the Black-Scholes equation, that are expressed as infinite series of reflections and Fourier series. Even for fixed barriers contracts different solutions give the same answer when all the terms have been added up but the rate of convergence of the sum to the solution can be quite different, depending on the time to expiry (maturity), i.e. the duration of the contract. Thus, we demonstrate the significance of the maturity parameter in option contracts when analytical methods like Fourier one is applied not only in jump-diffusion models.