An indirect inference method is implemented for a class of stochastic volatility models for financial data based on non-Gaussian Ornstein-Uhlenbeck (OU) processes. First, a quasi-likelihood estimator is derived from an approximative Gaussian state space representation of the OU model. Next, data are simulated from the OU model for given parameter values. The indirect inference estimator is then obtained by minimizing, in a weighted mean squared error sense, the score vector of the quasi-likelihood function for the simulated data, when this score vector is evaluated at the quasi-likelihood estimator obtained from the real data. The method is applied to Euro/Norwegian krone (NOK) and US Dollar/NOK daily exchange rate data. A simulation study reveals that the quasi-likelihood estimator may have a large bias even in large samples, but that the indirect inference estimator substantially reduces this bias. The accompanying R-package, which interfaces C++ code, is documented and can be downloaded. (C) 2011 Elsevier B.V. All rights reserved.