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Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads

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  • Peña, Javier
  • Vera, Juan C.
  • Zuluaga, Luis F.

Abstract

We study the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the bid–ask prices of vanilla call options in the underlying securities. We show that this semi-infinite problem can be recast as a linear program whose size is linear in the input data size. These developments advance previous related results, and enhance the practical value of static-arbitrage bounds as a pricing technique by taking into account the presence of bid–ask spreads. We illustrate our results by computing upper bounds on the price of a DJX basket option. The MATLAB code used to compute these bounds is available online at www.andrew.cmu.edu/user/jfp/arbitragebounds.html.

Suggested Citation

  • Peña, Javier & Vera, Juan C. & Zuluaga, Luis F., 2012. "Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads," European Journal of Operational Research, Elsevier, vol. 222(2), pages 369-376.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:2:p:369-376
    DOI: 10.1016/j.ejor.2012.04.035
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    References listed on IDEAS

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    1. 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.
    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.
    3. Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
    4. Li Chen & Simai He & Shuzhong Zhang, 2011. "Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection," Operations Research, INFORMS, vol. 59(4), pages 847-865, August.
    5. Peter Laurence & Tai-Ho Wang, 2008. "Distribution-free upper bounds for spread options and market-implied antimonotonicity gap," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 717-734.
    6. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    7. 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.
    8. 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.
    9. Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
    10. Peter Laurence & Tai-Ho Wang, 2005. "Sharp Upper and Lower Bounds for Basket Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 253-282.
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    3. Evangelia Dragazi & Shuaiqiang Liu & Antonis Papapantoleon, 2024. "Improved model-free bounds for multi-asset options using option-implied information and deep learning," Papers 2404.02343, arXiv.org.
    4. Wong, Man Hong & Zhang, Shuzhong, 2014. "On distributional robust probability functions and their computations," European Journal of Operational Research, Elsevier, vol. 233(1), pages 23-33.

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