The Pricing Of Reset Options Driven By Exponential Ornstein-Uhlenback Process

In the middle of seventies of last century, option as a financial derivative product occursin Amercian finacial market.Since then, it has been developed rapidly as an effectivemeans against risk and speculating. In order to attract the interest of invertors, manyfinancial companies gave rise to different type of options. In recent years, as financialmarkets continued to develop and improve, the standard options do not satisfy. marketdemand. To meet the needs of the financial market and increase financial market riskmanagement tools, has produced a variety of exotic options. Exotic options performancevariation in the terms and conditions and the occurrence of certain changes in its non-standard options on the complexity of the decision;the other hand, the prices of optionsdepend on the stock price fluctuation, therefore, Stock prices also decided to follow themodel of the complex nature of the complexity of the pricing options. Empirical studiesdemonstrate that the expected rate of return is often volatile, it may be dependent on thefunction of time and the stock price, therefore,The pricing of reset options by ExponentialOrnstein-Uhlenback process driven stock price is based on this consideration. Thereare two main ways about the pricing of derivative securities: First, partial differentialequations, Constructing that a derivative securities prices are satisfied with the appropriateboundary conditions of partial differential equations;Martingale Asset Pricing is anotherway, It wrote the value of the securities under the risk-neutral measure of the expectationsand the use of probabilistic methods payment discount terms. Martingale option pricingmethod in solving complex problems is very effective, this method is used.In this thesis, we mainly discuss prieing problems of reset options driven by ExponentialOrnstein - Uhlenbeek process. In the case of complete markets, we discuss four differentreset options respectively: reset pull, bear market reset pull warrants, reset call and bullmarket reset call warrants, and obtain the pricing formulas for these reset options byusing the methods of martingale and stochastic analysis. The main results are:1. In Chapter 2, we prove the pricing formula at time t of reset pull driven by Equation(1.2)(see Theorem2.1 below), and disceus the change of value and risk characteristics.2. In Chapter 3, we prove the pricing formula at time t of bear market reset pullwarrants driven by Equation (1.5) (Theorem3.1, Corollary3.2), and disccus the change of value and risk characteristics.3. In Chapter 4, under stochastic interest and nonstochastic interest, weprove the pricing formulas at time t of reset call driven by Equation(1.5) (Theo-rem4.1,Theorem4.6,Theorem4.7,Corollary4.3), and discuss the change of value and riskcharacteristics.4. In Chapter 5, with the help of Gisanov theorem and without Girsanov theorem,weprove the pricing formulas at time t of bull market reset call warrants driven by Equa-tion(1.5) (Theorem5.2,Theorem5.4).