IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1107.5720.html
   My bibliography  Save this paper

An algorithm for calculating the set of superhedging portfolios in markets with transaction costs

Author

Listed:
  • Andreas Lohne
  • Birgit Rudloff

Abstract

We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward in the event tree. We reformulate the problem as a sequence of linear vector optimization problems and solve it by adapting known algorithms. The corresponding superhedging strategy can be obtained going forward in the tree. Examples are given involving multiple correlated assets and basket options. Furthermore, we relate existing algorithms for the calculation of the scalar superhedging price to the set-valued algorithm by a recent duality theory for vector optimization problems. The main contribution of the paper is to establish the connection to linear vector optimization, which allows to solve numerically multi-asset superhedging problems under transaction costs.

Suggested Citation

  • Andreas Lohne & Birgit Rudloff, 2011. "An algorithm for calculating the set of superhedging portfolios in markets with transaction costs," Papers 1107.5720, arXiv.org, revised Dec 2013.
    • Handle: RePEc:arx:papers:1107.5720
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1107.5720
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/5630 is not listed on IDEAS
    2. repec:crs:wpaper:9513 is not listed on IDEAS
    3. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    4. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(1), pages 87-100, March.
    5. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    6. Patrick Cheridito & Michael Kupper, 2011. "Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 137-162.
    7. Perrakis, Stylianos & Lefoll, Jean, 1997. "Derivative Asset Pricing with Transaction Costs: An Extension," Computational Economics, Springer;Society for Computational Economics, vol. 10(4), pages 359-376, November.
    8. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    9. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    10. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alet Roux & Tomasz Zastawniak, 2013. "American options with gradual exercise under proportional transaction costs," Papers 1308.2688, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    2. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Jan 2015.
    3. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    4. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
    5. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    6. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
    7. Zachary Feinstein & Birgit Rudloff, 2018. "Time consistency for scalar multivariate risk measures," Papers 1810.04978, arXiv.org, revised Nov 2021.
    8. Jörn Sass & Manfred Schäl, 2014. "Numeraire portfolios and utility-based price systems under proportional transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 195-234, October.
    9. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
    10. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org, revised May 2021.
    11. Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 692-708, August.
    12. Bentahar, Imen & Bouchard, Bruno, 2005. "Explicit characterization of the super-replication strategy in financial markets with partial transaction costs," SFB 649 Discussion Papers 2005-053, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Jan Kallsen & Johannes Muhle-Karbe, 2011. "Existence of shadow prices in finite probability spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 251-262, April.
    15. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    16. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.
    17. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
    18. Zachary Feinstein & Birgit Rudloff, 2012. "Multiportfolio time consistency for set-valued convex and coherent risk measures," Papers 1212.5563, arXiv.org, revised Oct 2014.
    19. Perrakis, Stylianos & Lefoll, Jean, 2000. "Option pricing and replication with transaction costs and dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1527-1561, October.
    20. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics and Capital Growth in Financial Markets with Frictions," Economics Discussion Paper Series 1815, Economics, The University of Manchester.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1107.5720. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.