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Risk Management of Nonstandard Basket Options with Different Underlying Assets

Authors


  • The authors acknowledge the financial support of the Institut de Finance Mathématiques de Montréal (IFM2), the National Science and Engineering Research Council of Canada (NSERC), and the Fonds Québécois de Recherche sur la Société et la Culture, (FQRSC). This study extends N. Ouertani's Ph.D. thesis on which Phelim P. Boyle, Michel Denault, and Pascal François have made very helpful suggestions. We also thank Nabil Tahani and Jean-Guy Simonato for their comments.

Correspondence author, Management Science Department, HEC Montréal, 3000 chemin de la Côte-Ste-Catherine, Montréal, Qc, Canada, H3T 2A7. Tel: 514-340-5627; Fax: 514-340-5634; e-mail: genevieve.gauthier@hec.ca

Abstract

Basket options are among the most popular products of the new generation of exotic options. They are particularly attractive because they can efficiently and simultaneously hedge a wide variety of intrinsically different financial risks and are flexible enough to cover all the risks faced by firms. Oddly, the existing literature on basket options considers only standard baskets where all underlying assets are of the same type and hedge the same kind of risk. Moreover, the empirical implementation of basket-option models remains in its early stages, particularly when the baskets contain different underlying assets. This study focuses on various steps for developing sound risk management of basket options. We first propose a theoretical model of a nonstandard basket option on commodity price with stochastic convenience yield, exchange rate, and domestic and foreign zero-coupon bonds in a stochastic interest rate setting. We compare the hedging performance of the extended basket option containing different underlying assets with that of a portfolio of individual options. The results show that the basket strategy is more efficient. We apply the maximum likelihood method to estimate the parameters of the basket model and the correlations between variables. Monte Carlo simulations are conducted to examine the performance of the maximum likelihood estimator in finite samples of simulated data. A real-data study for a nonfinancial firm is presented to illustrate ways practitioners could use the extended basket option. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:299-326, 2013

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