This project takes as its starting point new theory for stochastic volatility models for financial data based on non-Gaussian (Ornstein-Uhlenbeck) diffusion processes. The project aims to contribute to the ongoing research activity in two ways: (i) to dev elop new methods and software for inference (estimation and prediction) and (ii) to apply these methods on daily exchange rate data for the Norwegian krone. In diffusion based stochastic volatility models, computation of the likelihood function requires n umerical integration in very high dimensions, which is infeasible in practice. Furthermore, Markov Chain Monte Carlo-based Bayesian methods may have poor convergence properties. In this project we will instead develop indirect inference methods which comb ine estimation of approximate state space models (with volatility as a latent varaible) with simulations from the underlying data generating model.