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Hedging Basket Options by Using a Subset of Underlying Assets

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  • Xia Su

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    Abstract

    This paper proposes two-step static hedging strategies for European basket options by using only plain-vanilla options on a subset of underlying assets. The basic idea is stimulated from a static super-hedging strategy dependent on the whole basket. However, it would be too complicated to handle when there is a large number of assets in the basket. It becomes even worse when some of the underlying assets are illiquid or not available for trading. Meanwhile, this strategy completely neglects the correlation structure of the basket which has indeed a great effect on the basket option's price. To solve these problems, Principal Components Analysis is used to figure out the subset of dominant assets through a careful study on the modified covariance of the basket. On this basis, the optimal strikes of those significant assets' plain-vanilla options are obtained in the second step via optimization. The optimality criterion depends on the risk attitude of hedgers and is defined by a certain risk measure, e.g., super-replication, minimum expected shortfall given a constraint on the hedging cost. Through analyzing a numerical example, it is concluded that this static hedging portfolio captures a trade-off between reduced hedging costs and overall super-replication. Even without considering transaction costs, hedging by using only a subset of underlying assets performs well: only a reasonable small hedging error arises when investing the capital required by the super-hedging portfolio which is composed of plain-vanilla options on all underlying assets and hence is difficult to implement or even not available in the market.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse14_2006.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse14_2006.

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    Length: 32
    Date of creation: Jun 2006
    Date of revision:
    Handle: RePEc:bon:bonedp:bgse14_2006

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    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: Basket options; Principal Components Analysis; Super-replication; Expected shortfall;

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    References

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    1. Paolo Pellizzari, 2003. "Static Hedging of Multivariate Derivatives by Simulation," Finance 0311013, EconWPA, revised 04 Dec 2003.
    2. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
    3. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
    4. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
    5. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
    6. Fengler, Matthias R. & Härdle, Wolfgang & Schmidt, Peter, 2001. "The analysis of implied volatilities," SFB 373 Discussion Papers 2001,73, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
    8. P. Pellizzari, 1998. "Efficient Monte Carlo Pricing of Basket Options," Finance 9801001, EconWPA.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    10. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    11. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
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