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

Schyns, Michael; Crama, Yves; Hübner, Georges

doi:10.1007/s10479-009-0636-y

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

Schyns, Michael; Crama, Yves; Hübner, Georges

2010 • In Annals of Operations Research, 181, p. 683-708

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https://hdl.handle.net/2268/76967

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10.1007/s10479-009-0636-y

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Keywords :

Value-at-Risk; Options; Operations Research

Abstract :

[en] 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.

Research center :

QuantOM

Disciplines :

Quantitative methods in economics & management

Author, co-author :

Schyns, Michael ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > UER Opérations : Informatique de gestion

Crama, Yves ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Recherche opérationnelle et gestion de la production

Hübner, Georges ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Gestion financière

Language :

English

Title :

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

Publication date :

2010

Journal title :

Annals of Operations Research

ISSN :

0254-5330

eISSN :

1572-9338

Publisher :

Springer Science & Business Media B.V.

Volume :

181

Pages :

683-708

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 24 November 2010

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