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

M. Schyns, Y. Crama, Georges Hübner

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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.

Original languageEnglish
Pages (from-to)683-708
Number of pages26
JournalAnnals of Operations Research
Volume181
Issue number1
DOIs
Publication statusPublished - Dec 2010

Keywords

  • STOCHASTIC-PROGRAMMING MODELS
  • ASSET/LIABILITY MANAGEMENT
  • CONTINGENT CLAIMS
  • GENERATION
  • TREE

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