IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1512.01527.html
   My bibliography  Save this paper

FX Options in Target Zone

Author

Listed:
  • Peter 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.

Suggested Citation

  • Peter Carr & Zura Kakushadze, 2015. "FX Options in Target Zone," Papers 1512.01527, arXiv.org, revised Jul 2016.
  • Handle: RePEc:arx:papers:1512.01527
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1512.01527
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dumas, Bernard & Peter Jennergren, L. & Naslund, Bertil, 1995. "Realignment risk and currency option pricing in target zones," European Economic Review, Elsevier, vol. 39(8), pages 1523-1544, October.
    2. Krugman,Paul & Miller,Marcus (ed.), 1992. "Exchange Rate Targets and Currency Bands," Cambridge Books, Cambridge University Press, number 9780521435260.
    3. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 06-83, Wharton School Rodney L. White Center for Financial Research.
    4. McKinnon, Ronald I, 1982. "Currency Substitution and Instability in the World Dollar Standard," American Economic Review, American Economic Association, vol. 72(3), pages 320-333, June.
    5. Robert P. Flood & Peter M. Garber, 1991. "The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 1367-1372.
    6. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2010. "Exchange Rate and Interest Rate Distribution and Volatility under the Portuguese Target Zone," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 57(3), pages 261-282, September.
    7. Klaster, Michel A. & Knot, Klaas H. W., 2002. "Toward an econometric target zone model with endogenous devaluation risk for a small open economy," Economic Modelling, Elsevier, vol. 19(4), pages 509-529, August.
    8. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    9. Bernd Kempa & Michael Nelles, 1999. "Misalignments of real exchange rates and the credibility of nominal currency bands," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 135(4), pages 613-628, December.
    10. Vlaar, Peter J G & Palm, Franz C, 1993. "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 351-360, July.
    11. Miller, Marcus & Weller, Paul, 1991. "Exchange Rate Bands with Price Inertia," Economic Journal, Royal Economic Society, vol. 101(409), pages 1380-1399, November.
    12. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    13. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    14. E.O. Svensson, Lars, 1994. "Why exchange rate bands? : Monetary independence in spite of fixed exchange rates," Journal of Monetary Economics, Elsevier, vol. 33(1), pages 157-199, February.
    15. John Williamson, 1986. "Target Zones and the Management of the Dollar," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 17(1), pages 165-174.
    16. de Jong, F, 1994. "A Univariate Analysis of EMS Exchange Rates Using a Target Zone Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(1), pages 31-45, Jan.-Marc.
    17. Dumas, Bernard & Jennergren, L. Peter & Naslund, Bertil, 1995. "Siegel's paradox and the pricing of currency options," Journal of International Money and Finance, Elsevier, vol. 14(2), pages 213-223, April.
    18. Rose, Andrew K & Svensson, Lars E O, 1995. " Expected and Predicted Realignments: The FF/DM Exchange Rate during the EMS, 1979-93," Scandinavian Journal of Economics, Wiley Blackwell, vol. 97(2), pages 173-200, June.
    19. Svensson, Lars E. O., 1991. "Target zones and interest rate variability," Journal of International Economics, Elsevier, vol. 31(1-2), pages 27-54, August.
    20. Lundbergh, Stefan & Terasvirta, Timo, 2006. "A time series model for an exchange rate in a target zone with applications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 579-609.
    21. Peter P. Carr & Robert A. Jarrow, 2008. "The Stop-Loss Start-Gain Paradox and Option Valuation: A new Decomposition into Intrinsic and Time Value," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    22. Dominquez, Kathryn M. & Kenen, Peter B., 1992. "Intramarginal intervention in the EMS and the target-zone model of exchange-rate behavior," European Economic Review, Elsevier, vol. 36(8), pages 1523-1532, December.
    23. Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
    24. Campa, Jose Manuel & Chang, P H Kevin, 1996. "Arbitrage-Based Tests of Target-Zone Credibility: Evidence from ERM Cross-Rate Options," American Economic Review, American Economic Association, vol. 86(4), pages 726-740, September.
    25. Bertola, Giuseppe & Caballero, Ricardo J, 1992. "Target Zones and Realignments," American Economic Review, American Economic Association, vol. 82(3), pages 520-536, June.
    26. Driffill, John & Sola, Martin, 2006. "Target zones for exchange rates and policy changes," Journal of International Money and Finance, Elsevier, vol. 25(6), pages 912-931, October.
    27. Klein, Michael W. & Lewis, Karen K., 1993. "Learning about intervention target zones," Journal of International Economics, Elsevier, vol. 35(3-4), pages 275-295, November.
    28. Anthony, Myrvin & MacDonald, Ronald, 1998. "On the mean-reverting properties of target zone exchange rates: Some evidence from the ERM," European Economic Review, Elsevier, vol. 42(8), pages 1493-1523, September.
    29. Bauer, Christian & De Grauwe, Paul & Reitz, Stefan, 2009. "Exchange rate dynamics in a target zone--A heterogeneous expectations approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 329-344, February.
    30. Mizrach, Bruce, 1995. "Target zone models with stochastic realignments: an econometric evaluation," Journal of International Money and Finance, Elsevier, vol. 14(5), pages 641-657, October.
    31. Svensson, Lars E. O., 1991. "The term structure of interest rate differentials in a target zone : Theory and Swedish data," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 87-116, August.
    32. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2013. "Exchange Rate Target Zones: A Survey Of The Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 27(2), pages 247-268, April.
    33. Edin, Per-Anders & Vredin, Anders, 1993. "Devaluation Risk in Target Zones: Evidence from the Nordic Countries," Economic Journal, Royal Economic Society, vol. 103(416), pages 161-175, January.
    34. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
    35. Meese, Richard A & Rose, Andrew K, 1990. "Nonlinear, Nonparametric, Nonessential Exchange Rate Estimation," American Economic Review, American Economic Association, vol. 80(2), pages 192-196, May.
    36. Kees G. Koedijk & Philip A. Stork & Casper G. De Vries, 1998. "An EMS target zone model in discrete time," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 31-48.
    37. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
    38. Svensson, Lars E. O., 1993. "Assessing target zone credibility : Mean reversion and devaluation expectations in the ERM, 1979-1992," European Economic Review, Elsevier, vol. 37(4), pages 763-793, May.
    39. Williamson, John, 1987. "Exchange rate flexibility, target zones, and policy coordination," World Development, Elsevier, vol. 15(12), pages 1437-1443, December.
    40. Antoine Magnier, 1992. "Théorie des zones cibles et fonctionnement du SME," Économie et Prévision, Programme National Persée, vol. 104(3), pages 87-113.
    41. Lin, Hwan C., 2008. "Forward-rate target zones and exchange rate dynamics," Journal of International Money and Finance, Elsevier, vol. 27(5), pages 831-846, September.
    42. Angel Serrat, 2000. "Exchange Rate Dynamics in a Multilateral Target Zone," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 193-211.
    43. Zhu, Zhen, 1996. "Persistent exchange-rate misalignment, noneconomic fundamentals and exchange-rate target zones," International Review of Economics & Finance, Elsevier, vol. 5(1), pages 1-19.
    44. Giuseppe Bertola & Lars E. O. Svensson, 1993. "Stochastic Devaluation Risk and the Empirical Fit of Target-Zone Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 689-712.
    45. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    46. Maurice Obstfeld & Kenneth Rogoff, 1995. "The Mirage of Fixed Exchange Rates," Journal of Economic Perspectives, American Economic Association, vol. 9(4), pages 73-96, Fall.
    47. Richard A. Meese & Andrew K. Rose, 1991. "An Empirical Assessment of Non-Linearities in Models of Exchange Rate Determination," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 603-619.
    48. Saphores, Jean-Daniel M., 2005. "The density of bounded diffusions," Economics Letters, Elsevier, vol. 86(1), pages 87-93, January.
    49. Svensson, Lars E. O., 1992. "The foreign exchange risk premium in a target zone with devaluation risk," Journal of International Economics, Elsevier, vol. 33(1-2), pages 21-40, August.
    50. Williamson, John, 1987. "Exchange Rate Management: The Role of Target Zones," American Economic Review, American Economic Association, vol. 77(2), pages 200-204, May.
    51. Edison, Hali J. & Miller, Marcus H. & Williamson, John, 1987. "On evaluating and extending the target zone proposal," Journal of Policy Modeling, Elsevier, vol. 9(1), pages 199-224.
    52. Cornell, Christopher M., 2003. "Target zones, reserve crises, and inverted S-curves," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 13(4), pages 313-323, October.
    53. Werner, Alejandro M., 1995. "Exchange rate target zones, realignments and the interest rate differential: Theory and evidence," Journal of International Economics, Elsevier, vol. 39(3-4), pages 353-367, November.
    54. Ball, Clifford A. & Roma, Antonio, 1994. "Target zone modelling and estimation for European Monetary System exchange rates," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 385-420, July.
    55. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    56. Kristian Stegenborg Larsen & Michael Sørensen, 2007. "Diffusion Models For Exchange Rates In A Target Zone," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 285-306, April.
    57. Ayuso, Juan & Restoy, Fernando, 1996. "Interest rate parity and foreign exchange risk premia in the ERM," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 369-382, June.
    58. Torres, Jose L., 2000. "An heterogeneous expectations target zone model," Economics Letters, Elsevier, vol. 67(1), pages 69-74, April.
    59. Lindberg, Hans & Soderlind, Paul, 1994. "Testing the basic target zone model on Swedish data 1982-1990," European Economic Review, Elsevier, vol. 38(7), pages 1441-1469, August.
    60. 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.
    61. Lai, Ching-chong & Fang, Chung-rou & Chang, Juin-jen, 2008. "Volatility trade-offs in exchange rate target zones," International Review of Economics & Finance, Elsevier, vol. 17(3), pages 366-379.
    62. Torres, Jose L., 2000. "Stochastic intramarginal interventions in target zones," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 10(3-4), pages 249-262, December.
    63. Lars E. O. Svensson, 1992. "An Interpretation of Recent Research on Exchange Rate Target Zones," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 119-144, Fall.
    64. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 6-83, Wharton School Rodney L. White Center for Financial Research.
    65. Dirk Veestraeten, 2008. "Valuing stock options when prices are subject to a lower boundary," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(3), pages 231-247, March.
    66. Chinn, Menzie David, 1991. "Some linear and nonlinear thoughts on exchange rates," Journal of International Money and Finance, Elsevier, vol. 10(2), pages 214-230, June.
    67. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    68. Rangvid, Jesper & Sorensen, Carsten, 2001. "Determinants of the implied shadow exchange rates from a target zone," European Economic Review, Elsevier, vol. 45(9), pages 1665-1696, October.
    69. Lindberg, Hans & Soderlind, Paul & Svensson, Lars E O, 1993. "Devaluation Expectations: The Swedish Krona 1985-92," Economic Journal, Royal Economic Society, vol. 103(420), pages 1170-1179, September.
    70. Sutherland, Alan, 1994. "Target Zone Models with Price Inertia: Solutions and Testable Implications," Economic Journal, Royal Economic Society, vol. 104(422), pages 96-112, January.
    71. Tronzano, Marco & Psaradakis, Zacharias & Sola, Martin, 2003. "Target zone credibility and economic fundamentals," Economic Modelling, Elsevier, vol. 20(4), pages 791-807, July.
    72. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    73. Paul Krugman & Marcus Miller, 1992. "Exchange Rate Targets and Currency Bands," NBER Books, National Bureau of Economic Research, Inc, number krug92-1, December.
    74. Taylor, Mark P. & Iannizzotto, Matteo, 2001. "On the mean-reverting properties of target zone exchange rates: a cautionary note," Economics Letters, Elsevier, vol. 71(1), pages 117-129, April.
    75. Williamson, John, 1989. "The Case for Roughly Stabilizing the Real Value of the Dollar," American Economic Review, American Economic Association, vol. 79(2), pages 41-45, May.
    76. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2013. "Exchange Rate Target Zones: A Survey Of The Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 27(2), pages 247-268, April.
    2. Lera, Sandro Claudio & Sornette, Didier, 2016. "Quantitative modelling of the EUR/CHF exchange rate during the target zone regime of September 2011 to January 2015," Journal of International Money and Finance, Elsevier, vol. 63(C), pages 28-47.
    3. Dumas, Bernard & Peter Jennergren, L. & Naslund, Bertil, 1995. "Realignment risk and currency option pricing in target zones," European Economic Review, Elsevier, vol. 39(8), pages 1523-1544, October.
    4. Jesús Rodríguez López & Hugo Rodríguez Mendizábal, 2007. "The Optimal Degree of Exchange Rate Flexibility: a Target Zone Approach," Review of International Economics, Wiley Blackwell, vol. 15(4), pages 803-822, September.
    5. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    6. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.
    7. Darvas, Zsolt, 1999. "Az árfolyamsávok empirikus modelljei és a devizaárfolyam sávon belüli előrejelezhetetlensége [Empirical models of exchange rate target zones]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 507-529.
    8. Bauer, Christian & De Grauwe, Paul & Reitz, Stefan, 2009. "Exchange rate dynamics in a target zone--A heterogeneous expectations approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 329-344, February.
    9. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2008. "Exchange Rate and Interest Rate Volatility in a Target Zone: The Portuguese Case," GEMF Working Papers 2008-03, GEMF, Faculty of Economics, University of Coimbra.
    10. Jesús Rodríguez López & Hugo Rodríguez Mendizábal, 2002. "On the Choice of an Exchange Regime: Target Zones Revisited," Economic Working Papers at Centro de Estudios Andaluces E2002/10, Centro de Estudios Andaluces.
    11. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    12. Jess Rodr?uez L?ez & Hugo Rodr?uez Mendiz?al, 2002. "On the Choice of an Exchange Rate Regime: Target Zones Revisited," UFAE and IAE Working Papers 518.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    13. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2012. "Testing for Nonlinear Adjustment in the Portuguese Target Zone: Is there a Honeymoon Effect?," GEMF Working Papers 2013-03, GEMF, Faculty of Economics, University of Coimbra.
    14. Jean-Pierre Laffargue & Sanvi Avouyi-Dovi, 1992. "Anticipations stabilisatrices dans un système de serpent monétaire. Théorie et application au système monétaire européen," Revue Économique, Programme National Persée, vol. 43(6), pages 1107-1128.
    15. 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.
    16. Pierdzioch, Christian, 2000. "The Effectiveness of the FX Market Interventions of the Bundesbank During the Louvre Period: An Options-Based Analysis," Kiel Working Papers 971, Kiel Institute for the World Economy (IfW).
    17. Dean Corbae & Christopher J. Neely & Paul A. Weller, 1998. "Endogenous realignments and the sustainability of a target," Working Papers 1994-009, Federal Reserve Bank of St. Louis.
    18. Jesús Crespo-Cuaresma & Balázs Egert & Ronald MacDonald, 2005. "Non-Linear Exchange Rate Dynamics in Target Zones: A Bumpy Road towards a Honeymoon - Some Evidence from the ERM, ERM2 and Selected New EU Member States," CESifo Working Paper Series 1511, CESifo.
    19. Vajanne, Laura, . "The Exchange Rate Under Target Zones," ETLA A, The Research Institute of the Finnish Economy, number 16, June.
    20. Lundbergh, Stefan & Terasvirta, Timo, 2006. "A time series model for an exchange rate in a target zone with applications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 579-609.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1512.01527. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.