Study On The Several Types Of New Options Pricing Problems Under Uncertain Environment

Option is an effective tool for hedging and avoiding risk. New options are derived from standard options. Correctly option pricing is the basis of taking on its function. The price of an option is influenced by many aspects. On the one hand, due to being disturbed by objective factors, some variables can not be accurately estimated by data, and some data by the observation and statistics will inevitably produce errors; On the other hand, people are always with subjective judgment when they will invest. Because new options are more complicated than standard options, the new options pricing problem are much more complex than standard options.Based on the traditional option pricing methods, this paper analyzes the existent methods are not all-inclusive, and we discover that the practical option pricing problem is always accompanied by the randomness and fuzziness. In 2009, European call and put option pricing formulas under uncertain environment are proposed by Liu. Comprehensively applying relative knowledge of uncertainty theory, on the basis of the assumption the price of underlying assets follows geometric canonical process, this paper gets some easy to use results for investors. By using of the MATLAB programs, we verify these results may provide some reference values for investors.This paper is structured as follows:First, we summarize the origin, development, models and methods of traditional option pricing theory. The second chapter introduces the relative knowledge of uncertainty theory. The following sections assume that the price of underlying assets follows geometric canonical process. Chapter III gets the pricing expressions of rainbow options under uncertain environment. In chapter IV, the barrier options pricing under uncertain environment are discussed; In the end, we study several kinds of spreads(Bull spreads, Bear spreads, Butterfly-shaped spread)and give some examples.