Pricing Of The Lookback Options Under Fuzzy Environments

With the new economy of China having moderated to a "new normal" pace,the financial market will face a new opportunity and challenge.As a short board in China’s financial market,the development of financial derivatives is very important for the stability of the financial market and the expansion of the financial market.Since the beginning of April 1973,for the first time since the option of trading on the Chicago Board Options Exchange,forty years options market development is very rapid.In the option contract,option price is only fluctuate with changes in market supply and demand quantity,so the option price will directly affect the sale income of both sides,which leads to the problem of option pricing has become the core problem in the financial derivatives market.In recent years,in the international financial derivatives market transactions,not only the most familiar European options,American options,but also a large number of exotic option derived from the standard options.The exotic option is a new combination of derivatives designers to meet the needs of investors and the market demand.The lookback option is one of the most popular exotic options.Because of the characteristics of the maximum return and the least regret,the price of the exotic option is relatively expensive.So it is very important to study the pricing of the option how to be more accurate.With the further development of option pricing,we find out that the financial environment that the option price depends on is very complex and fuzzy.This includes the subjective and objective factors in two aspects: subjective,affected by the risk preferences of investors,and so on;objectively,by the policy and market and other non random uncertainty.Subjective factors can not be avoided,but in order to deal with the objective of the non random uncertainty,we will add the new fuzzy mathematical theory in the option pricing model.It is also a new area of finance that has emerged in recent years.In this article,based on the traditional Black-Scholes option pricing model[2],through summing up and drawing on the experience at home and abroad,we decided to try to use the triangular fuzzy numbers and the extension principle as tools,introduced the theory of fuzzy mathematics to lookback option pricing.Ane then transformed it into optimization problems,and calculated it by bisection search algorithm,finally we got the fuzzy option price of lookback options.Finally,investors can choose whether or not to accept the option price by judging if they can accept the credibility,and make investment choices.In the model,the main consideration of the fuzzy pricing model of European lookback option with floating strike price,and then it can general inference to the pricing model of European lookback option pricing model of the fixed strike price and lookback option with partial observation.