The Pricing For A Class Of Barrier Options Under Non-Fuzzy Or Fuzzy Condition

The pricing for financial derivatives is among the most important problems of financial engineering. It dates back to L. Bachelier's degree paper " Theorie de la Speculation " in 1900. In his paper, the pricing for options was introduced and studied. With the perfection of financial market, more and more exotic options come up. Now, the pricing for these financial derivatives is becoming a hot problem in current finance.In this paper, we discuss the pricing for a class of barrier options which have a single barrier under non-fuzzy or fuzzy condition. In chapter 2, we derive pricing formulas for the class of barrier options under non-fuzzy condition by applying traditional pricing method. Owing to the pricing problem is a model abstracted from social phenomena. The environment which it can exist and develop in is social environment that is uncertain, complex and fuzzy. And the thought of the man who make judgement on the model is uncertain, too. In view of these facts, the fuzzy sets theory which was proposed by Zadeh may be a useful tool for modeling this kind of imprecise problem. It makes the model more realistic. Then, in chapter 3, we consider the fuzzy interest rate, fuzzy volatility and fuzzy stock price, and discuss the pricing for the class of barrier options under fuzzy condition. So, we propose the fuzzy pattern of the pricing formulas. Finally, we give a example.