Estimation in Stochastic Differential Equations with a State Dependent Diffusion Term

Abstract The most widely used methods for estimating parameters in stochastic differential equations, where the discrete time observations are corrupted with white noise, are based on (extended) Kalman filtering techniques for calculating the one-step prediction errors. Such methods cannot be used directly for estimation of parameters in stochastic differential equations (SDE) with a state dependent diffusion term. This paper describes a general transformation for some univariate SDEs that eliminates the state dependent diffusion term using the Ito formula. By employing this transformation the methods based on the Kalman filter techniques may still be used. Using simulation it is demonstrated that the approach leads to practically the same results as if a second order filter was used on the original SDE. As a case study a SDE describing the short term interest rate is studied.