This thesis aims to address the Kusuoka approximation (K-approximation) within the Gatheral model using Yamada’s method, also known as the Gaussian K-approximation. Our approach begins by transforming the original Gatheral model into a model with independent Wiener processes through Cholesky decomposition. Subsequently, the system is reformulated into its Stratonovich form, facilitating the definition of vector fields and their exponentials. We will assess whether the system satisfies the Uniformly Finitely Generated (UFG) condition. Additionally, based on our calculations, a simulation code will be developed to compare our results with those obtained by Yamada.