A Central Bank Strategy for Defending a Currency Peg

11 Pages Posted: 17 Dec 2019 Last revised: 2 Apr 2020

See all articles by Eyal Neuman

Eyal Neuman

Imperial College London

Alexander Schied

University of Waterloo

Chengguo Weng

University of Waterloo

Xiaole Xue

Shandong University

Date Written: December 15, 2019

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.

Keywords: currency target zone, currency peg, price impact, central bank intervention, singular stochastic control, second-order differential equation with infinite boundary conditions

Suggested Citation

Neuman, Eyal and Schied, Alexander and Weng, Chengguo and Xue, Xiaole, A Central Bank Strategy for Defending a Currency Peg (December 15, 2019). Available at SSRN: https://ssrn.com/abstract=3497807 or http://dx.doi.org/10.2139/ssrn.3497807

Eyal Neuman

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Alexander Schied (Contact Author)

University of Waterloo ( email )

200 University Ave W
Waterloo, Ontario
Canada

Chengguo Weng

University of Waterloo ( email )

M3-200 Univ Ave W
Waterloo, Ontario N2L3G1
Canada
(1)888-4567 ext.31132 (Phone)

Xiaole Xue

Shandong University ( email )

27 Shanda Nanlu
South Rd.
Jinan, Shandong 250100
China

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