IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v16y2016i6p929-945.html
   My bibliography  Save this article

Partial hedging and cash requirements in discrete time

Author

Listed:
  • Erdnç Akyildirim
  • Albert Altarovici

Abstract

This paper develops a discrete time version of the continuous time model of Bouchard et al. [ J. Control Optim. , 2009, 48 , 3123--3150], for the problem of finding the minimal initial data for a controlled process to guarantee reaching a controlled target with probability one. An efficient numerical algorithm, based on dynamic programming, is proposed for the quantile hedging of standard call and put options, exotic options and quantile hedging with portfolio constraints. The method is then extended to solve utility indifference pricing, good-deal bounds and expected shortfall problems.

Suggested Citation

  • Erdnç Akyildirim & Albert Altarovici, 2016. "Partial hedging and cash requirements in discrete time," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 929-945, June.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:6:p:929-945
    DOI: 10.1080/14697688.2015.1095347
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2015.1095347
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2015.1095347?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Naik, Vasanttilak & Uppal, Raman, 1994. "Leverage Constraints and the Optimal Hedging of Stock and Bond Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(2), pages 199-222, June.
    2. Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
    3. Peter Lindberg, 2010. "Optimal partial hedging in a discrete-time market as a knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 433-451, December.
    4. PInar, Mustafa Ç. & Salih, AslIhan & CamcI, Ahmet, 2010. "Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming," European Journal of Operational Research, Elsevier, vol. 201(3), pages 770-785, March.
    5. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    6. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
    7. Antonio E. Bernardo & Olivier Ledoit, 2000. "Gain, Loss, and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 144-172, February.
    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. Peter Lindberg, 2012. "Optimal partial hedging of an American option: shifting the focus to the expiration date," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 221-243, June.
    2. 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.
    3. Aliprantis, Charalambos D. & Polyrakis, Yiannis A. & Tourky, Rabee, 2002. "The cheapest hedge," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 269-295, July.
    4. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
    5. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2015, January-A.
    6. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21, July-Dece.
    7. Aliprantis, Charalambos D. & Tourky, Rabee, 2002. "Markets that don't replicate any option," Economics Letters, Elsevier, vol. 76(3), pages 443-447, August.
    8. Aliprantis, C. D. & Brown, D. J. & Werner, J., 2000. "Minimum-cost portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1703-1719, October.
    9. Huang, Kevin X. D., 2002. "On infinite-horizon minimum-cost hedging under cone constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 283-301, December.
    10. Sara Biagini & Mustafa Pinar, 2012. "The best gain-loss ratio is a poor performance measure," Papers 1209.6439, arXiv.org, revised Dec 2012.
    11. Chen, Yingshan & Dai, Min & Xu, Jing & Xu, Mingyu, 2015. "Superhedging under ratio constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 250-264.
    12. Marroquı´n-Martı´nez, Naroa & Moreno, Manuel, 2013. "Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?," European Journal of Operational Research, Elsevier, vol. 225(3), pages 429-442.
    13. Akuzawa, Toshinao & Nishiyama, Yoshihiko, 2013. "Implied Sharpe ratios of portfolios with options: Application to Nikkei futures and listed options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 335-357.
    14. Jun Sekine, 2002. "On superhedging under delta constraints," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 103-121.
    15. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    16. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    17. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Jun 2013.
    18. Regis Houssou & Olivier Besson, 2010. "Indifference of Defaultable Bonds with Stochastic Intensity models," Papers 1003.4118, arXiv.org.
    19. Gikas Hardouvelis & George Papanastasopoulos & Dimitrios D. Thomakos & Tao Wang, 2007. "Accruals, Net Stock Issues and Value-Glamour Anomalies: New Evidence on their Relation," Working Paper series 47_07, Rimini Centre for Economic Analysis.
    20. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.

    More about this item

    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:taf:quantf:v:16:y:2016:i:6:p:929-945. 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/RQUF20 .

    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.