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A central bank strategy for defending a currency peg

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  • Eyal Neuman
  • Alexander Schied
  • Chengguo Weng
  • Xiaole Xue

Abstract

We consider a central bank strategy for maintaining a two-sided currency target zone, in which an exchange rate of two currencies is forced to stay between two thresholds. To keep the exchange rate from breaking the prescribed barriers, the central bank is generating permanent price impact and thereby accumulating inventory in the foreign currency. Historical examples of failed target zones illustrate that this inventory can become problematic, in particular when there is an adverse macroeconomic trend in the market. We model this situation through a continuous-time market impact model of Almgren--Chriss-type with drift, in which the exchange rate is a diffusion process controlled by the price impact of the central bank's intervention strategy. The objective of the central bank is to enforce the target zone through a strategy that minimizes the accumulated inventory. We formulate this objective as a stochastic control problem with random time horizon. It is solved by reduction to a singular boundary value problem that was solved by Lasry and Lions (1989). Finally, we provide numerical simulations of optimally controlled exchange rate processes and the corresponding evolution of the central bank inventory.

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  • Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, arXiv.org.
    • Handle: RePEc:arx:papers:2008.00470
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    References listed on IDEAS

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    1. 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.
    2. Abel Cadenillas & Fernando Zapatero, 2000. "Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 141-156, April.
    3. 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.
    4. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    5. Eyal Neuman & Alexander Schied, 2018. "Protecting Pegged Currency Markets from Speculative Investors," Papers 1801.07784, arXiv.org, revised Feb 2021.
    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. Monique Jeanblanc‐Picqué, 1993. "Impulse Control Method and Exchange Rate," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 161-177, April.
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    10. Ralf Korn, 1997. "Optimal Impulse Control When Control Actions Have Random Consequences," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 639-667, August.
    11. 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.
    12. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
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    Cited by:

    1. Eyal Neuman & Alexander Schied, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.

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