We propose new modules in programming environment MATHEMATICA for the Black-Scholes model taking into account the sensitivity coefficients and considering discrete dividends taxed at rate tax. Then Black Scholes model with Leland corrections is presented in the case when we have discrete dividends and discrete taxes. The modules presented in this talk are component of web-based application, realized in the program environmental with central mathematical kernel and in some sense realizes the problem proposed above, and the build software instruments can be used for research investigations, as well as for training.