Research On Pricing Some Options Based On Uncertainty Theory

As we well known,financial derivatives are very important in modern finance.The option is one of the most popular financial derivatives instruments and it has attracted extensive attention and application.However,with the development of the financial market,vanilla options,such as European and American options,have many limitation resulting from their lack of flexibility.Under this background,exotic options,such as Asian options,lookback options,barrier options etc,emerged and developed rapidly.Options(both vanilla options and exotic options)pricing,has become one of the focus issue discussed by the scholars.The research on the option pricing in the traditional finance theory is based on the assumption that the price of underlying assets follows the stochastic differential equation.Behavioral finance is an innovation and development of the tradition finance and it is also the most important research field of financial investment theory.On the view of behavioral finance,the underlying asset price change does not like randomness.And some research results have shown that the assumption that the underlying asset follows a normal distribution is inconsistent with the actual.In fact,investors' belief degrees usually play an important role in real financial practice.In 2007,Liu founded a branch of axiomatic mathematics for modeling belief degrees?uncertainty theory.Furthermore,the uncertainty theory is introduced into the financial field,then the uncertain financial theory is formed.In this dissertation,we propose a new uncertain interest rate?stock price model based on the uncertainty theory.We deduce the pricing formulas of vanilla options such as European option and American option,and exotic options such as Asian option,lookback option and power option etc in the new uncertain interest rate?stock price stock model by applying the extreme value theorems and the time integral theorems etc.We obtain the pricing formulas of one-clique option and barrier option in the new uncertain interest rate?stock price stock model by applying Yao?Chen formula.At last,we analyze the price sensitivity of the European option in Liu model.