An Explicit Mapping of Currency Target Zone Models to Option Prices*

Date01 December 2019
AuthorDidier Sornette,Sandro Claudio Lera
Published date01 December 2019
An Explicit Mapping of Currency
Target Zone Models to Option
Singapore-ETH Centre, ETH Zurich, Singapore, Singapore
Department of Management, Technology, and Economics, ETH Zurich, Zurich,
Switzerland and
Swiss Finance Institute, University of Geneva, Geneva, Switzerland
Currency target zones have been under scrutiny for the past three decades,
which led to the development of two broad classes of quantitative models:
Phenomenological ones that explicitly take into consideration the markets
perception of the bounded exchange rate, and more mechanical ones that
rely on put and call options. Until now, the two models have only been com-
pared qualitatively. Here, we derive, for the rst time, a quantitative link
between these two approaches. Specically, we show how the former
approach has to be generalized in order to recover the second one. This map-
ping lets us relate the phenomenological parameter of the rst approach to
economically well-known quantities.
JEL Codes: E50; E51; E52; E58
Accepted: 12 April 2018
Currency target zones conne a countrys domestic currency within a prespeci-
ed upper and/or lower boundary with respect to some other currency. To
achieve this, the central bank pledges to intervene and either buy or sell its
currency, as soon as it touches the upper or lower boundary, respectively. Such
target zones (TZs) have been employed frequently in the 1990s in preparation
of the euro, and are still in use today. The TZ can be either single-sided, such as
* The research performed by Lera was conducted at the Future Resilient Systems at the Singapore-
ETH Centre (SEC). The SEC was established as a collaboration between ETH Zurich and the National
Research Foundation (NRF) Singapore (FI 370074011) under the auspices of the NRFs Campus for
Research Excellence and Technological Enterprise (CREATE) programme.
© 2018 International Review of Finance Ltd. 2018
International Review of Finance, 19:4, 2019: pp. 919927
DOI: 10.1111/ir.12196

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