ORPIT: A Matlab Toolbox for Option Replication and Portfolio Insurance in Incomplete Markets. In this work, we present the ORPIT Matlab toolbox. ORPIT applies the theory of vector lattices to solve (a) the problem of option replication and (b) the cost minimization problem of portfolio insurance as well as related sub problems. The key point is that we use the theory of lattice-subspaces and the theory of positive bases, in Riesz spaces, so ORPIT does not require the presence of linear programming methods. This is a great advantage of this approach that allows us to find multiple, if any, solutions of the corresponding problems after one call of the proposed methods. We illustrate the diverse features of the ten Matlab functions inside this toolbox through a representative collection of examples. To the best of our knowledge, there is no such solver to apply in problems of portfolio optimization or option replication.