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Optimal selection of a portfolio of options under Value-at-Risk constraints: a scenario approach

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  • M. Schyns
  • Y. Crama
  • G. Hübner

Abstract

This paper introduces a multiperiod model for the optimal selection of a financial portfolio of options linked to a single index. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its Value-at-Risk. We rely on scenarios to represent future security prices. The model contains several interesting features, like the consideration of transaction costs, bid-ask spreads, arbitrage-free option pricing, and the possibility to rebalance the portfolio with options introduced at the start of each period. The resulting mixed integer programming model is applied to realistic test instances involving options on the S&P500 index. In spite of the large size and of the numerical difficulty of this model, near-optimal solutions can be computed by a standard branch-and-cut solver or by a specialized heuristic. The structure and the financial features of the selected portfolios are also investigated. Copyright Springer Science+Business Media, LLC 2010

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  • M. Schyns & Y. Crama & G. Hübner, 2010. "Optimal selection of a portfolio of options under Value-at-Risk constraints: a scenario approach," Annals of Operations Research, Springer, vol. 181(1), pages 683-708, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:683-708:10.1007/s10479-009-0636-y
    DOI: 10.1007/s10479-009-0636-y
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    1. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    2. Yiu, K. F. C., 2004. "Optimal portfolios under a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1317-1334, April.
    3. Kouwenberg, Roy, 2001. "Scenario generation and stochastic programming models for asset liability management," European Journal of Operational Research, Elsevier, vol. 134(2), pages 279-292, October.
    4. Muzzioli, S. & Torricelli, C., 2005. "The pricing of options on an interval binomial tree. An application to the DAX-index option market," European Journal of Operational Research, Elsevier, vol. 163(1), pages 192-200, May.
    5. Gulpinar, Nalan & Rustem, Berc & Settergren, Reuben, 2004. "Simulation and optimization approaches to scenario tree generation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1291-1315, April.
    6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    7. Pieter Klaassen, 1998. "Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/Liability Management: A Synthesis," Management Science, INFORMS, vol. 44(1), pages 31-48, January.
    8. Kallio, Markku & Ziemba, William T., 2007. "Using Tucker's theorem of the alternative to simplify, review and expand discrete arbitrage theory," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2281-2302, August.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    11. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
    12. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    13. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," European Journal of Operational Research, Elsevier, vol. 101(2), pages 374-392, September.
    14. M. Gilli & E. Kellezi & H. Hysi, 2006. "A Data-Driven Optimization Heuristic for Downside Risk Minimization," Computing in Economics and Finance 2006 355, Society for Computational Economics.
    15. Philippe Bertrand & Jean-Luc Prigent, 2005. "Portfolio Insurance Strategies: OBPI versus CPPI," Post-Print hal-01833077, HAL.
    16. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    17. Cees Dert & Bart Oldenkamp, 2000. "Optimal Guaranteed Return Portfolios and the Casino Effect," Operations Research, INFORMS, vol. 48(5), pages 768-775, October.
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    Cited by:

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    2. An Chen & Thai Nguyen & Mitja Stadje, 2018. "Risk management with multiple VaR constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 297-337, October.
    3. Akhter Mohiuddin Rather, 2012. "Portfolio selection using mean-risk model and mean-risk diversification model," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 14(3), pages 324-342.

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