Aortic valvuloplasty is a minimally invasive procedure for the dilatation of stenotic aortic valves. Rapid ventricular pacing is an established technique for balloon stabilization during this procedure. However, low cardiac output due to the pacing is one of the inherent risks, which is also associated with several potential complications. This paper proposes a numerical modelling approach to understand the effect of different inflation levels of a valvuloplasty balloon catheter on the positional instability caused by a pulsating blood flow. An unstretched balloon catheter model was crimped into a tri-folded configuration and inflated to several levels. Ten different inflation levels were then tested, and a Fluid-Structure Interaction model was built to solve interactions between the balloon and the blood flow modelled in an idealised aortic arch. Our computational results show that the maximum displacement of the balloon catheter increases with the inflation level, with a small step at around 50% inflation and a sharp increase after reaching 85% inflation. This work represents a substantial progress towards the use of simulations to solve the interactions between a balloon catheter and pulsating blood flow.