This chapter deals with an extension to the developed novel cubature methods of degrees 5 on Wiener space. It examines cubature formulae that are exact for all multiple Stratonovich integrals up to dimension equal to the degree. Cubature method reduces solving a stochastic differential equation to solving a finite set of ordinary differential equations. The chapter aims to compare the numerical solutions with the Black's and Black–Scholes models' analytical solutions. It examines the convergence of the sequences of constructed trinomial model to a geometric Brownian motion. The chapter also examines the conditions that make the probability measure in our trinomial model a martingale measure, i.e. risk-neutral probability measure. The constructed model has practical usage in pricing American options and American-style derivatives. The chapter emphasizes that the constructed trinomial tree has practical usage and applications in pricing path-dependent and American-style options.