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

• Date: 01 December 2019
• Author: Didier Sornette,Sandro Claudio Lera
• DOI: http://doi.org/10.1111/irfi.12196
• Published date: 01 December 2019

An Explicit Mapping of Currency

Target Zone Models to Option

Prices*

SANDRO CLAUDIO LERA

†,‡

AND DIDIER SORNETTE

‡,§

†

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

ABSTRACT

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 market’s

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 first time, a quantitative link

between these two approaches. Specifically, 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 first approach to

economically well-known quantities.

JEL Codes: E50; E51; E52; E58

Accepted: 12 April 2018

I. INTRODUCTION

Currency target zones confine a country’s domestic currency within a prespeci-

fied 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 NRF’s Campus for

Research Excellence and Technological Enterprise (CREATE) programme.

© 2018 International Review of Finance Ltd. 2018

International Review of Finance, 19:4, 2019: pp. 919–927

DOI: 10.1111/irfi.12196