IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v6y1999i2p61-85.html
   My bibliography  Save this article

A hybrid method for pricing European options based on multiple assets with transaction costs

Author

Listed:
  • Graziella Pacelli
  • Maria Cristina Recchioni
  • Francesco Zirilli

Abstract

The problem of pricing European options based on multiple assets with transaction costs is considered. These options include, for example, quality options and options on the minimum of two or more risky assets. The value of these options is the solution of a nonlinear parabolic partial differential equation subject to a final condition given by the payoff function associated with the option. A computationally efficient method to solve this final-value problem is proposed. This method is based on an asymptotic expansion of the required solution with respect to the parameters related to the transaction costs followed by the numerical solution of the linear partial differential equations obtained at each order in perturbation theory. The numerical solution of these linear problems involves an implicit finite-difference scheme for the parabolic equation and the use of the fast Fourier sine transform to solve the resulting elliptic problems. Numerical results obtained on test problems with the method proposed here are shown and discussed.

Suggested Citation

  • Graziella Pacelli & Maria Cristina Recchioni & Francesco Zirilli, 1999. "A hybrid method for pricing European options based on multiple assets with transaction costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 61-85.
    • Handle: RePEc:taf:apmtfi:v:6:y:1999:i:2:p:61-85
    DOI: 10.1080/135048699334555
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334555
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/135048699334555?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 337-356, October.
    3. 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.
    4. C. Atkinson & P. Wilmott, 1995. "Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 357-367, October.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    2. Dichtl, Hubert & Drobetz, Wolfgang, 2011. "Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1683-1697, July.
    3. Lin, Zih-Ying & Chang, Chuang-Chang & Wang, Yaw-Huei, 2018. "The impacts of asymmetric information and short sales on the illiquidity risk premium in the stock option market," Journal of Banking & Finance, Elsevier, vol. 94(C), pages 152-165.
    4. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    5. Al–Zhour, Zeyad & Barfeie, Mahdiar & Soleymani, Fazlollah & Tohidi, Emran, 2019. "A computational method to price with transaction costs under the nonlinear Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 291-301.
    6. Baule, Rainer & Münchhalfen, Patrick & Shkel, David & Tallau, Christian, 2023. "Fair-washing in the market for structured retail products? Voluntary self-regulation versus government regulation," Journal of Banking & Finance, Elsevier, vol. 148(C).
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    9. Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.
    10. Li, Ming-Yuan Leon, 2008. "Clarifying the dynamics of the relationship between option and stock markets using the threshold vector error correction model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 511-520.
    11. 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.
    12. Kanne, Stefan & Korn, Olaf & Uhrig-Homburg, Marliese, 2016. "Stock Illiquidity, option prices, and option returns," CFR Working Papers 16-08, University of Cologne, Centre for Financial Research (CFR).
    13. Clewlow, Les & Hodges, Stewart, 1997. "Optimal delta-hedging under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1353-1376, June.
    14. Joao Amaro de Matos & Paula Antao, 2000. "Market illiquidity and the Bid-Ask spread of derivatives," Nova SBE Working Paper Series wp386, Universidade Nova de Lisboa, Nova School of Business and Economics.
    15. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    16. Kyungsub Lee & Byoung Ki Seo, 2021. "Analytic formula for option margin with liquidity costs under dynamic delta hedging," Papers 2103.15302, arXiv.org.
    17. Entrop, Oliver & Fischer, Georg, 2019. "Hedging costs and joint determinants of premiums and spreads in structured financial products," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe B-34-19, University of Passau, Faculty of Business and Economics.
    18. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    19. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    20. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..

    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:taf:apmtfi:v:6:y:1999:i:2:p:61-85. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.