Option Evaluation Approach with Continuous Fuzzy Volatility Variable in Risk Management

This paper aim is to formulate a random fuzz process for the fuzzy volatility and evaluate options by fuzzy simulation. Some basic definitions of fuzzy variable and random fuzzy differential equation are reviewed. Option pricing formula for fuzzy financial markets based on Liu fuzzy theory is given. Fuzzy simulation technique is designed to estimate the membership degree and the expected value of the option. The rough figures of the expected value of option can be obtained. The fuzzy put-call parity relationship is proposed in this paper. Finally, the application of the methodology is demonstrated by a numerical example.