In this paper, authors will compare the small open economy model with incomplete and complete asset markets and their steady states that depend on initial conditions and equilibrium dynamics. In the literature, to induce stationarity in these models, some changes have been proposed for the standard model. This paper presents a quantitative comparison of these alternative approaches for stationarity of these models. Here, three different specifications model, which lead to stationarity in the model, are considered: (1) A model with a debt-elastic interest rate premium; (2) A model with convex portfolio adjustment costs; (3) A model with complete asset markets. The main finding of the paper is that all the models create almost same dynamics in business-cycle frequencies, as measured by unconditional second moments and impulse response functions. The only noticeable difference between the alternative specifications is that the complete-asset-market model induces smoother consumption dynamics. Also, altering the parameters which led to stationarity, within a wide range around the baseline initial value does not affect significantly on the predictions of the dynamics of the model.