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A Continuous‐Time Model for Valuing Foreign Exchange Options

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  • James J. Kung

Abstract

This paper makes use of stochastic calculus to develop a continuous‐time model for valuing European options on foreign exchange (FX) when both domestic and foreign spot rates follow a generalized Wiener process. Using the dollar/euro exchange rate as input for parameter estimation and employing our FX option model as a yardstick, we find that the traditional Garman‐Kohlhagen FX option model, which assumes constant spot rates, values incorrectly calls and puts for different values of the ratio of exchange rate to exercise price. Specifically, it undervalues calls when the ratio is between 0.70 and 1.08, and it overvalues calls when the ratio is between 1.18 and 1.30, whereas it overvalues puts when the ratio is between 0.70 and 0.82, and it undervalues puts when the ratio is between 0.86 and 1.30.

Suggested Citation

  • James J. Kung, 2013. "A Continuous‐Time Model for Valuing Foreign Exchange Options," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:635746
    DOI: 10.1155/2013/635746
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    References listed on IDEAS

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    1. Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. "The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-840, June.
    2. 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..
    3. 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.
    4. 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.
    5. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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