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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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    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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