The aim of the paper is to fulfill the gap for testing hypotheses on parameters of the Stochastic Volatility model, more precisely, to propose finite-sample exact tests in the sense that the tests have correct levels. To do this, we examine method-of-moments-based tests and explicit expressions are available for the estimators, simplifying highly the test procedures. We then state the asymptotic distribution of the estimator as well as that of the proposed test statistics for testing the null hypothesis of no-persistence in the volatility. We then compare in a study of level and power these asymptotic techniques to the technique of Monte Carlo tests which is valid in finite samples.