Pricing currency options based on fuzzy techniques.

*(English)*Zbl 1153.91544
Eur. J. Oper. Res. 193, No. 2, 530-540 (2009); retraction ibid. 201, No. 3, 971 (2010).

Summary: Owing to the fluctuation of financial markets from time to time, some financial variables can always be observed with perturbations and be expected in the imprecise sense. Therefore, this paper starts from the fuzzy environments of currency options markets, introduces fuzzy techniques, and gives a fuzzy currency options pricing model. By turning exchange rate, interest rates and volatility into 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 their later use. In order to obtain the belief degree, an optimization procedure has been applied. An empirical study is performed based on daily foreign exchange market data. The empirical study results indicate that the fuzzy currency options pricing method is a useful tool for modeling the imprecise problem in the real world.

Editorial remark: The paper has been retracted by the Editor-in-Chief [ibid. 201, No. 3, 971 (2010; Zbl 1173.91391)] because parts of this paper are identical to [H.-Ch. Wu, Comput. Oper. Res. 31, No. 7, 1069–1081 (2004; Zbl 1062.91041)].

Editorial remark: The paper has been retracted by the Editor-in-Chief [ibid. 201, No. 3, 971 (2010; Zbl 1173.91391)] because parts of this paper are identical to [H.-Ch. Wu, Comput. Oper. Res. 31, No. 7, 1069–1081 (2004; Zbl 1062.91041)].