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The Pricing of Call and Put Options on Foreign Exchange

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Author Info
Orlin J. Grabbe
Abstract

This paper derives exact pricing equations for American and European puts and calls on foreign exchange and discusses hedging strategy. Because every call option on foreign currency is simultaneously a put option on the domestic currency, an equivalence relation exists that allows the immediate derivation of put equations from the corresponding call formulas. The call and put pricing formulas are unlike the Black-Scholes equations for stock options in that there are two relevant interest rates, interest rates are stochastic, and boundary constraints differ. In addition, both American call and put options have values larger than their European counterparts.

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Paper provided by Wharton School Rodney L. White Center for Financial Research in its series Rodney L. White Center for Financial Research Working Papers with number 06-83.

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Handle: RePEc:fth:pennfi:06-83

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  1. Michael Schmutz, 2008. "Semi-static hedging for certain Margrabe type options with barriers," Quantitative Finance Papers 0810.5146, arXiv.org. [Downloadable!]
  2. Jérôme B. Detemple, 1999. "American Options: Symmetry Properties," CIRANO Working Papers 99s-45, CIRANO. [Downloadable!]
  3. Gabriele Galati & Patrick Higgins & Owen F. Humpage & William Melick, 2006. "Option prices, exchange market intervention, and the higher moment expectations channel: a user’s guide," Working Paper 0618, Federal Reserve Bank of Cleveland. [Downloadable!]
    Other versions:
  4. Christian Pierdzioch, 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. [Downloadable!]
  5. Kleopatra Nikolaou & Lucio Sarno, 2005. "New Evidence on the Forward Unbiasedness Hypothesis in the Foreign Exchange Market," Money Macro and Finance (MMF) Research Group Conference 2005 77, Money Macro and Finance Research Group. [Downloadable!]
  6. Bernard Dumas & L. Peter Jennergren & Bertil Naslund, 1993. "Realignment Risk and Currency Option Pricing in Target Zones," NBER Working Papers 4458, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. Richard K. Lyons, 1986. "Tests of the foreign exchange risk premium using the expected second moments implied by option pricing," International Finance Discussion Papers 290, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  8. Frey, Rüdiger & Daniel Sommer, 1995. "A Systematic Approach to Pricing and Hedging of International Derivatives with Interest-Rate Risk," Discussion Paper Serie B 306, University of Bonn, Germany, revised Jun 1996. [Downloadable!]
  9. Ilya Molchanov & Michael Schmutz, 2008. "Geometric extension of put-call symmetry in the multiasset setting," Quantitative Finance Papers 0806.4506, arXiv.org, revised Mar 2009. [Downloadable!]
  10. Garry de Jager, 1991. "A Note on Parameters in Binomial Option Pricing," Working Paper Series 2, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  11. Mark Broadie & Jérôme B. Detemple, 1996. "American Options on Dividend-Paying Assets," CIRANO Working Papers 96s-16, CIRANO. [Downloadable!]
  12. Vivek Bhargava, Robert Brooks, D.K. Malhotra, 2001. "Implied volatilities, stochastic interest rates, and currency futures options valuation: an empirical investigation," European Journal of Finance, Taylor and Francis Journals, vol. 7(3), pages 231-246, September. [Downloadable!] (restricted)
  13. Frank Lehrbass, 1994. "Optimal hedging with currency forwards, calls, and calls on forwards for the competitive exporting firm facing exchange rate uncertainty," Journal of Economics, Springer, vol. 59(1), pages 51-70, February. [Downloadable!] (restricted)
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