Pricing Of Double Barrier Knock-out Options

With the development of theories of financial mathematics,the tools of mathematics are applied more and more widely in the financial products.The financial derivatives based on the mathematical model are also increasing.The classical forwards,futures,options,swaps could not meet the investors and managers of risk's needs.Some financial derivatives with special properties have been come up with.This paper mainly studies the pricing problems of barrier option that is one type of the exotic options.The usual unilateral barrier options,in order to help the investors stop loss or prevent extravagant premium,is only being set one barrier for becoming effective or losing efficiency at the time of touching the barrier.The double barrier knock-out options which we study in this thesis is in a complex case where the options lose efficiency when pass through two or more barrier levels in turn in accordance with the fixed path.The constant boundaries are consider in this thesis.We assume that the volatility and risk-free rate of interest are constant,and the pricing of underlying assets follows geometric Brownian motions.Firstly,under the condition that the initial price exceeds the upper boundary,we discuss the case where the underlying assets take effect when the price of underlying assets reach the upper boundary.The underlying assets lose efficiency when the price reach the upper boundary and reach the lower boundary in turn.Another case we considered is that the initial price below the lower boundary.We discuss the case where the underlying assets take effect when the price of underlying assets knock-in from the lower boundary and lose efficiency when reach upper and lower boundary twice and knock-out from the upper boundary.By Black-Scholes formula.Girsanov principle and Ito-Doeblin formula,we obtain the pricing formula for the double boundary knock-out barrier options.In practice,we can draw on the experience of these models and study how to protect the investors' income about the strongly active assets when price has shrunk seriously.