Securitization of Financial Assets: Approximation in Theory and Practice

Abstract

Asset-Backed Securitization (ABS) is an emerging sector of today banks' business. It represents an effective tool to turn unrated assets, such as commercial papers or lease contracts, into marketable financial products through the issuance of special notes, namely the asset-backed securities.

In this paper we analyze the problem of optimally selecting the assets to be converted into notes with respect to scenarios motivated by real-world problems. In particular, we study the case in which the assets amortization rule is characterized by constant periodic principal installments instead of the more classical amortization rule based on constant general (principal plus interests) installments. We show the computational advantages and the practical implications of this choice. The particular shape of the outstanding principal for the case of constant principal installments is exploited in the solution of a general model which selects assets at different dates.

Four approximation algorithms, based on LP-relaxation and on the implicit knapsack structure of the problem, are proposed for this general model. From a theoretical point of view we analyze the exact worst-case behavior of these algorithms compared to the optimal solution. Computational experiments are performed for a practical scenario suggested by a leasing bank. The results show that the proposed approximation algorithms are, on average, highly efficient and effective.