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A Jump‐diffusion Model for Exchange Rates in a Target Zone

Author

Listed:
  • F. De Jong
  • F. C. Drost
  • B. J. M. Werker

Abstract

We propose a simple jump‐diffusion model for an exchange rate target zone. The model captures most stylized facts from the existing target zone models while remaining analytically tractable. The model is based on a modified two‐limit version of the COX, INGERSOLL and ROSS (1985) model. In the model the exchange rate is kept within the band because the variance decreases as the exchange rate approaches the upper or lower limits of the band. We also consider an extension of the model with parity adjustments, which are modeled as Poisson jumps. Estimation of the model is by GMM based on conditional moments. We derive prices of currency options in our model, assuming that realignment jump risk is idiosyncratic. Throughout, we apply the theory to EMS exchange rate data. We show that, after the EMS crisis of 1993, currencies remain in an implicit target zone which is narrower than the officially announced target zones.

Suggested Citation

  • F. De Jong & F. C. Drost & B. J. M. Werker, 2001. "A Jump‐diffusion Model for Exchange Rates in a Target Zone," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 270-300, November.
    • Handle: RePEc:bla:stanee:v:55:y:2001:i:3:p:270-300
    DOI: 10.1111/1467-9574.00170
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    Cited by:

    1. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    2. Hui, Cho-Hoi & Lo, Chi-Fai & Fong, Tom Pak-Wing, 2016. "Swiss franc's one-sided target zone during 2011–2015," International Review of Economics & Finance, Elsevier, vol. 44(C), pages 54-67.
    3. Taiga Saito, 2016. "Pricing Foreign Exchange Options Under Intervention by Absorption Modeling," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(1), pages 85-106, March.
    4. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    5. Bessec, Marie, 2003. "Mean-reversion vs. adjustment to PPP: the two regimes of exchange rate dynamics under the EMS, 1979-1998," Economic Modelling, Elsevier, vol. 20(1), pages 141-164, January.
    6. Lo, C.F. & Hui, C.H. & Fong, T. & Chu, S.W., 2015. "A quasi-bounded target zone model — Theory and application to Hong Kong dollar," International Review of Economics & Finance, Elsevier, vol. 37(C), pages 1-17.
    7. Giorgio Ferrari & Tiziano Vargiolu, 2020. "On the singular control of exchange rates," Annals of Operations Research, Springer, vol. 292(2), pages 795-832, September.
    8. C. H. Hui & C. F. Lo & T. Fong, 2015. "A Quasi-Bounded Model for Swiss Franc's One-Sided Target Zone During 2011-2015," Working Papers 152015, Hong Kong Institute for Monetary Research.
    9. Guangli Xu & Shiyu Song & Yongjin Wang, 2016. "The Valuation Of Options On Foreign Exchange Rate In A Target Zone," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-19, May.
    10. Cho-Hoi Hui & Chi-Fai Lo & Po-Hon Chau, 2017. "Can Exchange Rate Dynamics in Krugman¡¯s Target-zone Model be Directly Tested?Abstract: Despite Krugman's (1991) model being a benchmark for modelling target zones, empirical support has been sparse d," Working Papers 032017, Hong Kong Institute for Monetary Research.
    11. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
    12. Damir Filipovi'c & Martin Larsson & Sergio Pulido, 2017. "Markov cubature rules for polynomial processes," Papers 1707.06849, arXiv.org, revised Jun 2019.
    13. Mancini, Cecilia, 2008. "Large deviation principle for an estimator of the diffusion coefficient in a jump-diffusion process," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 869-879, May.
    14. Huimin Zhao & Fuzhou Gong & Fangping Peng & Qin Liu, 2014. "Probability Analysis of Exchange Rate Target Zones," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 5(1), pages 29-41, January.
    15. Ferrari, Giorgio, 2018. "On a Class of Singular Stochastic Control Problems for Reflected Diffusions," Center for Mathematical Economics Working Papers 592, Center for Mathematical Economics, Bielefeld University.
    16. Martin Diviš, 2017. "Options valuation included jumps in intervention period [Oceňování opcí se zahrnutím skoků v období intervencí]," Český finanční a účetní časopis, Prague University of Economics and Business, vol. 2017(3), pages 19-38.
    17. Sandun Perera & Winston Buckley & Hongwei Long, 2018. "Market-reaction-adjusted optimal central bank intervention policy in a forex market with jumps," Annals of Operations Research, Springer, vol. 262(1), pages 213-238, March.
    18. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.

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