IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1801.07784.html
   My bibliography  Save this paper

Protecting Pegged Currency Markets from Speculative Investors

Author

Listed:
  • Eyal Neuman
  • Alexander Schied

Abstract

We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity arises from a local time along a random curve. Our first result identifies a certain local time as that central bank strategy for which this risk position is minimized. We then consider the worst-case situation the central bank may face by identifying that strategy of the strategic investor that maximizes the expected inventory of the central bank under a cost criterion, thus establishing a Stackelberg equilibrium in our model.

Suggested Citation

  • Eyal Neuman & Alexander Schied, 2018. "Protecting Pegged Currency Markets from Speculative Investors," Papers 1801.07784, arXiv.org, revised Feb 2021.
  • Handle: RePEc:arx:papers:1801.07784
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1801.07784
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. de Jong, F, 1994. "A Univariate Analysis of EMS Exchange Rates Using a Target Zone Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(1), pages 31-45, Jan.-Marc.
    2. Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    3. Svensson, Lars E. O., 1991. "The term structure of interest rate differentials in a target zone : Theory and Swedish data," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 87-116, August.
    4. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    5. Bertola, Giuseppe & Caballero, Ricardo J, 1992. "Target Zones and Realignments," American Economic Review, American Economic Association, vol. 82(3), pages 520-536, June.
    6. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    7. Clifford Ball & Antonio Roma, 1998. "Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 1-15.
    8. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    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. Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, 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. Eyal Neuman & Alexander Schied, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.
    2. Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    3. Eyal Neuman & Alexander Schied, 2015. "Optimal Portfolio Liquidation in Target Zone Models and Catalytic Superprocesses," Papers 1504.06031, arXiv.org, revised Jul 2015.
    4. Forde, Martin & Kumar, Rohini & Zhang, Hongzhong, 2015. "Large deviations for the boundary local time of doubly reflected Brownian motion," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 262-268.
    5. Beetsma, Roel M. W. J., 1995. "EMS exchange rate bands: a Monte Carlo investigation of three target zone models," Journal of International Money and Finance, Elsevier, vol. 14(2), pages 311-328, April.
    6. Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, arXiv.org.
    7. Elliott, Robert & Qiu, Jinniao & Wei, Wenning, 2022. "Neumann problem for backward SPDEs with singular terminal conditions and application in constrained stochastic control under target zone," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 68-97.
    8. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2013. "Exchange Rate Target Zones: A Survey Of The Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 27(2), pages 247-268, April.
    9. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    10. Jesús Rodríguez López & Hugo Rodríguez Mendizábal, 2007. "The Optimal Degree of Exchange Rate Flexibility: a Target Zone Approach," Review of International Economics, Wiley Blackwell, vol. 15(4), pages 803-822, September.
    11. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.
    12. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    13. Ribeiro de Castro, Claudia, 1999. "Inside and Outside the Band Exchange Rate Fluctuations for Brazil," LIDAM Discussion Papers IRES 2000004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    14. Miller, J. Isaac & Park, Joon Y., 2005. "How They Interact to Generate Persistency in Memory," Working Papers 2005-01, Rice University, Department of Economics.
    15. Jess Rodr?uez L?ez & Hugo Rodr?uez Mendiz?al, 2002. "On the Choice of an Exchange Rate Regime: Target Zones Revisited," UFAE and IAE Working Papers 518.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    16. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
    17. Taylor, Mark P. & Iannizzotto, Matteo, 2001. "On the mean-reverting properties of target zone exchange rates: a cautionary note," Economics Letters, Elsevier, vol. 71(1), pages 117-129, April.
    18. Marie Bessec, 2000. "Mean-Reversion versus PPP Adjustment: The Two Regimes of Exchange Rate Dynamics Under the EMS, 1979-1998," Econometric Society World Congress 2000 Contributed Papers 1305, Econometric Society.
    19. Mundaca, Gabriela, 2003. "A Drift of the "Drift Adjustment Method"," Memorandum 16/2002, Oslo University, Department of Economics.
    20. Jean-Pierre Laffargue & Sanvi Avouyi-Dovi, 1992. "Anticipations stabilisatrices dans un système de serpent monétaire. Théorie et application au système monétaire européen," Revue Économique, Programme National Persée, vol. 43(6), pages 1107-1128.

    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:1801.07784. 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.