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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 635746, 10 pages
http://dx.doi.org/10.1155/2013/635746
Research Article

A Continuous-Time Model for Valuing Foreign Exchange Options

School of Management, Ming Chuan University, Taipei 111, Taiwan

Received 12 February 2013; Accepted 20 May 2013

Academic Editor: Qun Lin

Copyright © 2013 James J. Kung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.