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This work intends to study the effect of aortic annulus eccentricity and leaflet rigidity on the performance, thrombogenic risk and calcification risk in bioprosthetic aortic valve replacements (BAVRs). To address these questions, a two‐way immersed fluid–structure interaction (FSI) computational model was implemented in a high‐performance computing (HPC) multi‐physics simulation software, and validated against a well‐known FSI benchmark. The aortic valve bioprosthesis model is qualitatively contrasted against experimental data, showing good agreement in closed and open states. Regarding the performance of BAVRs, the model predicts that increasing eccentricities yield lower geometric orifice areas (GOAs) and higher normalized transvalvular pressure gradients (TPGs) for healthy cardiac outputs during systole, agreeing with in vitro experiments. Regions with peak values of residence time are observed to grow with eccentricity in the sinus of Valsalva, indicating an elevated risk of thrombus formation for eccentric configurations. In addition, the computational model is used to analyze the effect of varying leaflet rigidity on both performance, thrombogenic and calcification risks with applications to tissue‐engineered prostheses. For more rigid leaflets it predicts an increase in systolic and diastolic TPGs, and decrease in systolic GOA, which translates to decreased valve performance. The peak shear rate and residence time regions increase with leaflet rigidity, but their volume‐averaged values were not significantly affected. Peak solid stresses are also analyzed, and observed to increase with rigidity, elevating risk of valve calcification and structural failure. To the authors' knowledge this is the first computational FSI model to study the effect of eccentricity or leaflet rigidity on thrombogenic biomarkers, providing a novel tool to aid device manufacturers and clinical practitioners. [ABSTRACT FROM AUTHOR]