Research On Pricing Financial Derivatives Based On Uncertainty Theory

Financial derivatives play an important role in modern financial markets, how to fairly price the financial derivatives is becoming more and more important. In traditional financial models and methods, the underlying asset price are described by some stochastic differential equations. However, with the rise of behavioral finance, more and more scholars realized that the asset price change does not like random-ness. Many other empirical findings in financial fields showed that using stochastic differential equation to describe the stock price is inappropriate, the distribution of underlying asset price is not consist with the assumption of normal probability dis-tribution from stochastic differential equation. In real financial practice, investors' belief degrees usually play an important role in decisions making and affect the finan-cial market performance. Uncertainty theory is a branch of axiomatic mathematics for modeling belief degrees founded by Liu in 2007, and subsequently it has been applied successfully in the study of finance. In this dissertation, we mainly study some pricing problems of financial derivatives in uncertain environment within the framework of uncertainty theory.Different from traditional Black-Scholes model in which the stock price is de-scribed by using a stochastic differential equation, our research is based on the assumption that the underlying asset price follow some uncertain differential equa-tions. Under the uncertain stock model and uncertain interest rate model, the pricing problems of geometric average Asian option, lookback option, power option, interest rate ceiling and floor, stock loan and convertible bonds are discussed in this dissertation, and the pricing formulas are derived by using uncertain calculus theory and method.In conclusion, the contributions of this dissertation are embodied in the follow-ing aspects:(1) The pricing problems of geometric average Asian option, lookback option and power option are firstly discussed within the framework of uncertainty theory, and under the uncertain stock model, the pricing formulas of geometric average Asian option, lookback option and power option are derived by using uncertain calculus theory and method;(2) The valuation of interest rate ceiling and floor is firstly studied based on uncertainty theory, and the pricing formulas under the uncertain interest rate model are given;(3) The pricing problem of stock loan is firstly investigated within the framework of uncertainty theory, and the pricing formulas under the uncertain stock model are presented;(4) The pricing problem of convertible bonds is firstly explored with the uncer-tainty theory, and the pricing formulas under uncertain stock model are obtained by the theory and method of uncertain calculus and uncertain differential equation.