Computational Optimization and Applications

, Volume 29, Issue 2, pp 147–171 | Cite as

Securitization of Financial Assets: Approximation in Theory and Practice

  • Renata Mansini
  • Ulrich Pferschy


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.

asset-backed securitization approximation algorithm knapsack problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Bertsimas and R. Demir, “An approximate dynamic programming approach to multidimensional knapsack problems,” Management Science, vol. 48, pp. 550–565, 2002.Google Scholar
  2. 2.
    P.C. Chu and J.E. Beasley, “A genetic algorithm for the multidimensional knapsack problem,” Journal of Heuristics, vol. 4, pp. 63–86, 1998.Google Scholar
  3. 3.
    T.H. Donaldson, Credit and Risk Exposure in Securitization and Transactions, Mac Millan, 1989.Google Scholar
  4. 4.
    S. Hanafi and A. Fréville, “An efficient tabu search approach for the 0-1 multidimensional knapsack problem,” European Journal of Operational Research, vol. 106, pp. 659–675, 1998.Google Scholar
  5. 5.
    J. Henderson and J.P. Scott, Securitization, Woodhead-Faulkner, 1988.Google Scholar
  6. 6.
    P. Kang and S.A. Zenios, “Complete prepayment models for mortgage-backed securities,” Management Science, vol. 38, pp. 1665–1685, 1992.Google Scholar
  7. 7.
    P. Kang and S.A. Zenios, “Mean-absolute deviation portfolio optimization for mortgage-backed securities,” Annals of Operations Research, vol. 45, pp. 433–450, 1993.Google Scholar
  8. 8.
    H. Kellerer and U. Pferschy, “A new fully polynomial time approximation scheme for the knapsack problem,” Journal of Combinatorial Optimization, vol. 3, pp. 59–71, 1999.Google Scholar
  9. 9.
    H. Kellerer and U. Pferschy, “Improved dynamic programming in connection with an FPTAS for the knapsack problem,” to appear in Journal of Combinatorial Optimization, vol. 8, 2004.Google Scholar
  10. 10.
    H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems, Springer, 2004.Google Scholar
  11. 11.
    R. Mansini, Mixed Integer Linear Programming Models for Financial Problems: Analysis, Algorithms and Computational Results, Ph.D. Thesis, Univ. of Bergamo, 1997 (in Italian).Google Scholar
  12. 12.
    R. Mansini and M.G. Speranza, “A multidimensional knapsack model for the asset-backed securitization,” Journal of the Operational Research Society, vol. 53, pp. 822–832, 2002.Google Scholar
  13. 13.
    R. Mansini and M.G. Speranza, “Selection of lease contracts in an asset-backed securitization: a real case analysis,” Control and Cybernetics, vol. 28, pp. 739–754, 2000.Google Scholar
  14. 14.
    S. Martello, D. Pisinger, and P. Toth, “Newtrends in exact algorithms for the 0-1 knapsack problem,” European Journal of Operational Research, vol. 123, pp. 325–332, 2000.Google Scholar
  15. 15.
    J.J. Norton, Asset Securitization: International Financial and Legal Perspectives, Blackwell, 1991.Google Scholar
  16. 16.
    H. Pirkul, “Aheuristic solution procedure for the multiconstraint zero–one knapsack problem,” Naval Research Logistics, vol. 34, pp. 161–172, 1987.Google Scholar
  17. 17.
    D. Pisinger, “A minimal algorithm for the 0-1 knapsack problem,” Operations Research, vol. 45, pp. 758–767, 1997.Google Scholar
  18. 18.
    E.S. Schwartz and W.N. Torous, “Prepayment and the valuation of mortgage-backed securities,” Journal of Finance, vol. 44, pp. 375–392, 1989.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Renata Mansini
    • 1
  • Ulrich Pferschy
    • 2
  1. 1.Department of Electronics for AutomationUniversity of BresciaBresciaItaly
  2. 2.Department of Statistics and Operations ResearchUniversity of GrazGrazAustria

Personalised recommendations