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FX options in target zones

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  • Peter P. Carr
  • Zura Kakushadze

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.
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  • Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:10:p:1477-1486
    DOI: 10.1080/14697688.2016.1238500
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    3. Zura Kakushadze & Willie Yu, 2019. "iCurrency?," Papers 1911.01272, arXiv.org, revised Nov 2019.
    4. Zura Kakushadze, 2020. "Option Pricing: Channels, Target Zones and Sideways Markets," Papers 2006.14121, arXiv.org.
    5. Peter Carr, 2017. "Bounded Brownian Motion," Risks, MDPI, vol. 5(4), pages 1-11, November.
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    7. Samuel Drapeau & Yunbo Zhang, 2019. "Pricing and Hedging Performance on Pegged FX Markets Based on a Regime Switching Model," Papers 1910.08344, arXiv.org, revised May 2020.
    8. Zura Kakushadze, 2020. "Option Pricing: Channels, Target Zones and Sideways Markets," Bulletin of Applied Economics, Risk Market Journals, vol. 7(2), pages 25-33.

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