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Protecting Pegged Currency Markets from Speculative Investors

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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