Study On The Finite Difference Method For Pricing A Double Barrier Option

Double barrier option is a type of exotic options, and has becoming a hotresearch field these years. It belongs to weak path-dependent options. It is also aspecial model for European options. Its final income level depends not only on theprice of the original assets at expiration of options contract, but also on whether theoriginal assets throughout the observation period of the option contract touch apredetermined price level, which is called barriers. It is necessary for double barrieroptions to set down both the upper and lower border barriers when the option contractis studied out. An option contract shall be terminated whenever the underlying assettouches the barriers, and both parties to the contract end the contract according to theprearranged terms.In this thesis, a quantitative analysis on pricing a double barrier option, which islinked the price of gold, is accomplished by using the finite difference method. First,the pricing a double barrier option discussed is a class of problem for determiningsolutions of second-order linear partial differential equations, and it is reduced to astandard set of determining solutions of homogeneous linear parabolic equationproblems with the variable substitution. Second, by the introduction of combineddifference quotient, a kind of three-layer seven-point explicit difference schemes withhigher order accuracy and a sort of three-layer nine-point implicit difference schemeswith higher order accuracy are given, and their convergence and stability areinvestigated. Finally, numerical examples are performed, which results show thatthese two difference methods are effective.