Bounds Pricing Method of Currency Options Based on Triangular Fuzzy Numbers, Fuzzy Programming and Fuzzy Regression

Some financial variables can always be observed with perturbations and be expected in the imprecise sense because of the fluctuation of financial markets. Therefore, this paper introduces fuzzy techniques, and gives a fuzzy currency options bounds pricing model. By denoting four input variables in the Garman-Kohlhagen model as triangular fuzzy numbers, the currency option price will turn into a fuzzy number. In order to construct easily the membership function of this fuzzy number, a triangular fuzzy number is used to approximate it. Then a fuzzy programming procedure is proposed to determine its lower bound and upper bound. Finally, the proposed fuzzy currency options bounds pricing model is tested with the daily market data of the EUR/USD currency option. The empirical study results indicate that the proposed method is a useful tool for modelling the imprecise problems in the foreign exchange derivative markets.