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

**Elisabeth Larsson
**

Division of Scientific Computing

Department of Information Technology

Uppsala University

Uppsala

### Abstract:

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.