Abstract
Foreign exchange rates have been subjected to periods of tighter or looser controls as various political and economic forces have waxed and waned. When currencies were backed by gold there were fixed exchange rates. In 1973 floating exchange rates were adopted though many countries did try to keep their currency values within certain ranges. More recently the European Economic Community formalized this practice. Free-floating exchange rates might be well characterized by the lognormal distribution which is standard in option pricing. However, this is probably a poor approximation for exchange rates which are kept within some range by the actions of one or both governments or central banks. This paper develops a model which can be used to value options and other derivative contracts when the underlying exchange rate is bounded in a fixed range (a, b). Methods for pricing both European and American style options are developed.
Similar content being viewed by others
References
Barone-Adesi, G., and R. E. Whaley. (1987). “Efficient Analytic Approximation of American Option Values,”The Journal of Finance 42, 301–320.
Black, F., and M. Scholes. (1973). “The Pricing of Options and Corporate Liabilities,”Journal of Political Economy 81, 637–654.
Cox, J. C., and S. A. Ross. (1976). “The Valuation of Options for Alternative Stochastic Processes,”Journal of Financial Economics 3, 145–166.
Cox, J. C., J. E. Ingersoll, Jr., and S. A. Ross. (1981). “The Relation Between Forward Prices and Futures Prices,”Journal of Financial Economics 9, 321–346.
Garman, M. B., and S. W. Kohlhagen. (1983). “Foreign Currency Option Values,”Journal of International Money and Finance 2, 231–238.
Giddy, I. (1983). “Foreign Exchange Options,”Journal of Futures Markets 3, 143–166.
Grabbe, J. O. (1983). “The Pricing of Call and Put Options on Foreign Exchange,”Journal of International Money ana Finance 2, 239–253.
Ingersoll, J. E., Jr. (1987).Theory of Financial Decision Making. Totowa. N.J.: Rowman & Littlefield.
Ingersoll, J. E., Jr. (1991). “An Approximation for Valuing American Puts and Other Financial Derivatives Using ‘Barrier’ Options,” unpublished working paper.
Karlin, S., and H. M. Taylor. (1981).A Second Course in Stochastic Processes. New York: Academic Press.
Lieu, D. (1990). “Option Pricing with Futures Style Margining,”Journal of Futures Markets 10, 327–338.
Merton, R. C. (1973). “Theory of Rational Option Pricing,”Bell Journal of Economics and Management Science 4, 141–183.
Merton, R. C. (1977). “On the Pricing of Contingent Claims and the Modigliani-Miller Theorem,”Journal of Financial Economics 5, 125–144.
Shastri, K., and K. Tandon. (1986). “On the Use of European Models to Price American Options on Foreign Currency,”Journal of Futures Markets 6, 93–108.
Author information
Authors and Affiliations
Additional information
The author would like to thank Ken French and Geert Rouwenhorst for their comments and suggestions.
Rights and permissions
About this article
Cite this article
Ingersoll, J.E. Valuing foreign exchange rate derivatives with a bounded exchange process. Rev Deriv Res 1, 159–181 (1996). https://doi.org/10.1007/BF01531597
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01531597