FX Options in Target Zone

Quantitative Finance 17(10) (2017) 1477-1486, Featured Article

25 Pages Posted: 6 Dec 2015 Last revised: 16 Sep 2017

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Date Written: June 21, 2016

Abstract

In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) short-rate is not deterministic. When the band is narrow, we can pick the functional form of the FX rate process based on computational convenience. With a thoughtful choice, the FX option pricing problem can be solved analytically. The European option prices are expressed via (fast converging) series of elementary functions. We discuss the general approach to solving the pricing PDE and explicit examples, including analytically tractable models with (non-Ornstein-Uhlenbeck) mean-reversion.

Keywords: FX, options, target zone, attainable boundaries, Brownian motion, volatility, drift, reflecting barriers

JEL Classification: G00

Suggested Citation

Carr, Peter P. and Kakushadze, Zura, FX Options in Target Zone (June 21, 2016). Quantitative Finance 17(10) (2017) 1477-1486, Featured Article. Available at SSRN: https://ssrn.com/abstract=2699250 or http://dx.doi.org/10.2139/ssrn.2699250

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

1127 High Ridge Road #135
Stamford, CT 06905
United States
6462210440 (Phone)
6467923264 (Fax)

HOME PAGE: http://www.linkedin.com/in/zurakakushadze

Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159
Georgia

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