Filtering and parameter estimation of partially observed diffusion processes using Gaussian RBFs

Elisabeth Larsson
Division of Scientific Computing
Department of Information Technology
Uppsala University


Financial asset prices can be modeled as stochastic diffusion processes involving a number of parameters. Based on market observations over time, we want to estimate these parameters. However, due to the so called ask-bid spread, there is an uncertainty in the observed data. We model the spread as additive noise, and show that using Gaussian radial basis functions (RBFs), leads to a convenient mathematical representation. Furthermore, substantial parts of the computations can be performed analytically if RBFs are used for approximating transition densities. We present numerical results for a short term interest rate model showing that we can generate a smooth likelihood surface.