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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, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:1:p:405-420
    DOI: 10.1111/mafi.12324
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    References listed on IDEAS

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    1. Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, arXiv.org.
    2. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    3. 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.
    4. 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.
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    7. Bertola, Giuseppe & Caballero, Ricardo J, 1992. "Target Zones and Realignments," American Economic Review, American Economic Association, vol. 82(3), pages 520-536, June.
    8. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
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    11. 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.
    12. Ralf Korn, 1997. "Optimal Impulse Control When Control Actions Have Random Consequences," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 639-667, August.
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    Cited by:

    1. Rama Cont & Alessandro Micheli & Eyal Neuman, 2022. "Fast and Slow Optimal Trading with Exogenous Information," Papers 2210.01901, arXiv.org, revised Jun 2023.

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