We present an exact method for solving non separable convex integer quadratic problems (IQP). Such problems arise in financial applications. The method we propose transforms (IQP) into a parameterized mixed linear integer problem which provides an overestimation of (IQP) depending on an integer parameter K. We show that as K gets larger, the overestimation tends to the optimal value of (IQP). The practical value of this approach is supported by numerical experiments. The asymptotic behavior of the method, associated with the determination of a precise feasible solution, allows us to exactly solve instances involving up to 60 bounded integer variables. We compare our computational results with the ones obtained by using a commercial solver (Cplex).