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Static Arbitrage Bounds on Basket Option Prices

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  • Alexandre d'Aspremont
  • Laurent El Ghaoui

Abstract

We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. Although this problem is very hard to solve exactly in the general case, we show that in some instances the upper and lower bounds can be computed via simple closed-form expressions, or linear programs. We also introduce an efficient linear programming relaxation of the general problem based on an integral transform interpretation of the call price function. We show that this relaxation is tight in some of the special cases examined before.

Suggested Citation

  • Alexandre d'Aspremont & Laurent El Ghaoui, 2003. "Static Arbitrage Bounds on Basket Option Prices," Papers math/0302243, arXiv.org, revised Oct 2005.
    • Handle: RePEc:arx:papers:math/0302243
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    File URL: http://arxiv.org/pdf/math/0302243
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    References listed on IDEAS

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    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    2. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    3. 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 637-654, May-June.
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    Cited by:

    1. J. A. Primbs, 2010. "SDP Relaxation of Arbitrage Pricing Bounds Based on Option Prices and Moments," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 137-155, January.
    2. Javier Pena & Juan Vera & Luis Zuluaga, 2010. "Static-arbitrage lower bounds on the prices of basket options via linear programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 819-827.

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