Abstract
We solve the problem of optimal securitization for an issuer facing heterogeneous investors with arbitrary time and risk preferences. We show that the optimal securitization is characterized by multiple nonlinear tranches, and each investor gets a portfolio of these tranches. In particular, when all agents have CARA utilities, the linear tranching is optimal, with the number of tranches being less than or equal to the number of investors. To the best of our knowledge, this is the first model in the literature that explains the appearance of multiple tranches in the security design and the relation of the tranche thresholds to microeconomic characteristics. We show that the boundaries of the tranches can be efficiently calculated through a fixed point of a contraction mapping, and we develop new powerful techniques that are generally applicable for numerical calculation of constrained Pareto-efficient allocations. We use these contraction mapping techniques to derive a number of comparative static results for optimal securitization. The model generates theoretical predictions and numerical simulations that agree with several recent empirical findings concerning the CDO structure.
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