The aim of the paper was to present two the most important valuation models of American call option. In the scientific literature such models are well known, but the way the final formulas of them are conducted are not clearly presented. The detailed analysis of relationship between variables included in the model was also shown. The added value of the paper is the “step-by-step” analytical calculation of the premium value of the Black & Scholes formula and also the way the “Greek numbers” were derived. The paper consists of four chapters in which two models of options valuation and the way of calculation of “Greek numbers” were derived.