On Some Properties of the Option Price Related to the Solution of the Black-Scholes Equation

Amnuay Kananthai, Ekkarath Thailert

Abstract

In functional analysis, the spectrum of the operators is the one of interests which having interesting properties. In this paper, we applied such spectrum to the option price which is the solution of the Black-Scholes equation. We found that such option price is contained in the spectrum. Moreover we can find the kernel of such the Black-Scholes equation. We also obtain the interesting properties of the kernel such as the expected value and variance. However the results of this paper will useful in the boarding of the research in the area of  financial mathematics.