Pricing the Foreign Currency Options with the Fuzzy Numbers Based on the Garman-Kohlhagen Model

摘要

This paper starts from the fuzzy environments of foreign currency options markets, introduces fuzzy sets theory, and gives a fuzzy version of Garman-Kohlhagen currency options pricing model. By taking exchange rate, domestic interest rate, foreign interest rate, and volatility as triangular fuzzy numbers, the currency option price will turn into a fuzzy number. This makes the financial investors who can pick any currency option price with an acceptable belief degree for the later use. In order to obtain the belief degree, an optimization procedure has been applied. An empirical study is performed based on market data. The study result indicates the fuzzy currency options pricing method is a useful tool for modeling the imprecise problem in the real world.