| Abstract [eng] |
The aim of research was to construct simple and effective weak approximations for the solution of the CKLS (Chan–Karolyi–Longstaff–Sanders) model that would use only generation of discrete random variables at each approximation step. CKLS model was introduced in 1992 and is widely used for modeling interest rates and prices of options and bonds. Particular cases of the model are the Vašiček model, a geometric Brownian motion, the CIR model, etc. The solution of the CKLS model is not known in explicit form, and therefore numerical methods are constructed. We construct first- and second-order weak approximations for the CKLS model using split-step, moments matching, and approximate moment matching techniques. We decompose the model into deterministic and stochastic parts, so that we need to construct a discretization scheme for the stochastic part only because the deterministic part is easily solvable in explicit way. Moment matching and approximate moments techniques allow us to approximate the former by discrete random variables. A certain composition of approximations of deterministic and stochastic parts gives weak approximations of the initial equation of the desired order. |
