FX Options in Target Zone

TL;DR

This paper explores analytical pricing of FX options within target zones with reflecting boundaries, highlighting how the no-arbitrage condition influences the FX rate process and providing explicit solutions for European options.

Contribution

It introduces a method to analytically price FX options in target zones with attainable, reflecting boundaries, considering the no-arbitrage condition and mean-reversion models.

Findings

European option prices expressed via converging series

Analytical solutions for models with mean-reversion

Pricing approach applicable to narrow bands

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.