Option pricing based on a type of fuzzy process

Liu process is a basic process in fuzzy environment. As an extension of Liu process, fractional Liu process has attracted the attention of many scholars. In this paper, a fuzzy stock model driven by fractional Liu process is established, and its European, American, Asian, power options pricing formulas are given. In order to better understand these formulas, we give a few numerical examples to illustrate the changes of European option price with different parameters when time is fixed. However, these examples are not based on real-life data since the lack of parameter estimation method for fuzzy differential equation driven by Liu process. Then the changes of American option price are given when time and parameters are both changed. At the same time, we study the parameter interval where the option price fluctuates greatly. Finally, the fuzzy stock model is extended to the generalized case, and the stock price is given.