Currency Target Zones as Mirrored Options

16 Pages Posted: 18 May 2017 Last revised: 18 Oct 2018

See all articles by Sandro Claudio Lera

Sandro Claudio Lera

MIT Media Lab

Matthias Leiss

ETH Zurich

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute

Date Written: May 16, 2017

Abstract

A new way of modeling the dynamics of an exchange rate target zone is presented. In the presence of a single upper (resp. lower) target boundary, the exchange rate is precisely represented as the sum of a free float and a short (resp. long) position in a call (resp. put) option with strike price at the boundary. To model a target zone (with two boundaries), a natural approach consists in describing the exchange rate dynamics as the combination of the two, namely the sum of free float together with a long position in a put written on the lower boundary and a short position in a call option written on the upper boundary, respectively. We show that this first order approximation leads to significant mispricing (as much as 20%) and must be iterated, leading to an infinite sequence of compounded 'mirrored' option prices. We analyze basic properties of such mirrored nested options analytically, describe how to calculate them numerically, and show why it is crucial to take into account higher order corrections in realistic target zones. We argue that this analogy to option prices allows for conceptually simple generalizations that describe different target zone arrangements. We apply our methodology to the estimation of the fundamental value of the Hong Kong dollar that is hidden by the target zone peg to the US dollar. We also estimate the implied maturity and explain how this parameter serves as direct proxy for target zone credibility.

Keywords: Exchange rate dynamics, Target zones, Compound options

JEL Classification: E50, E51, E52, E58

Suggested Citation

Lera, Sandro Claudio and Leiss, Matthias and Sornette, Didier, Currency Target Zones as Mirrored Options (May 16, 2017). Available at SSRN: https://ssrn.com/abstract=2969663 or http://dx.doi.org/10.2139/ssrn.2969663

Sandro Claudio Lera (Contact Author)

MIT Media Lab ( email )

77 Massachusetts Avenue
Cambridge, MA 02139
United States

Matthias Leiss

ETH Zurich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Register to save articles to
your library

Register

Paper statistics

Downloads
94
rank
269,963
Abstract Views
739
PlumX Metrics