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
Date Written: June 21, 2016
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: Suggested Citation