  Given the importance of continuous-time stochastic volatility models to
describe the dynamics of interest rates, we propose a goodness-of-fit test for
the parametric form of the drift and diffusion functions, based on a marked
empirical process of the residuals. The test statistics are constructed using a
continuous functional (Kolmogorov-Smirnov and Cram\'er-von Mises) over the
empirical processes. In order to evaluate the proposed tests, we implement a
simulation study, where a bootstrap method is considered for the calibration of
the tests. As the estimation of diffusion models with stochastic volatility
based on discretely sampled data has proven difficult, we address this issue by
means of a Monte Carlo study for different estimation procedures. Finally, an
application of the procedures to real data is provided.
