Optimal Securitization with Heterogeneous Investors

66 Pages Posted: 4 Mar 2010 Last revised: 16 Mar 2010

See all articles by Semyon Malamud

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Huaxia Rui

University of Rochester - Simon Business School

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management

Date Written: March 2, 2010

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.

Keywords: securitization, tranching, heterogeneity, mortgage backed securities, asset backed securities

JEL Classification: G32, G21, G24

Suggested Citation

Malamud, Semyon and Rui, Huaxia and Whinston, Andrew B., Optimal Securitization with Heterogeneous Investors (March 2, 2010). Swiss Finance Institute Research Paper No. 10-10, Available at SSRN: https://ssrn.com/abstract=1563522 or http://dx.doi.org/10.2139/ssrn.1563522

Semyon Malamud (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Huaxia Rui

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management ( email )

CBA 5.202
Austin, TX 78712
United States
512-471-8879 (Phone)

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