| Abstract [eng] |
In financial mathematics, CIR process is widely used for modeling interest rates. Mackevicius [5] proposed, instead, to use the stochastic Verhulst process. The main its disadvantage is that explicit expressions of moments are not known. Therefore, the moment closure condition q(t) = EX^2_t /EX_t was proposed. Baravykas in his master thesis [1] analyzed q(t) approximations by the method of partial sums of Fourier series. In this diploma project, first, we continue research in this direction by optimizing freely chosen parameters and simplifying calculations. Second, using the same properties of partial sums of Fourier series, we construct a new q(t) approximation that gives more accurate results and is easily implemented. For calculations, we use the statistical package R. |
