Some Study Of The Barrier Options Pricing Problems

Options are the core tool of risk management.Early in 1973,Fischer Black and Myron Scholes proposed a famous option pricing model - Black-Scholes model.Afterwards following years,option pricing theory has developed quickly.Recently,in addition to known European options and American options, there appear many new variety which are changed,composed,derived by vanilla options in international financial market.Barrier options are one of these new options.Barrier options are cheaper than standard European options,so they are welcome to market.They are widely applied in risk management.This thesis focuses on the study of barrier options pricing.And this thesis is composed of the following five chapters:In chapter 1,the emergence and development of option pricing theory , the history of barrier options and the main contents of this thesis are introduced.In chapter 2,firstly, the pricing problems of vanilla European options and modified European options are introduced.Then ,on the assumption that volatility a,dividend q and risk-free rate r are the function of time t and there have transaction costs in mar-ket,European options are discussed.And their pricing formulae and call-put parity are presented.In chapter 3,the pricing problems of eight kinds of European barrier options are discussed,their pricing formulae and call-put parity are derived and barrier options call-put symmetry are analyzed in section one.In section two,according to the position of initial stock price S0,double barrier options are divided into two types. And their pricing problems are studied.We find double barrier options are composed of either one single barrier option and one double out option or two single barrier options.Thus the pricing problems of double barrier options are transformed to the pricing problems of single barrier options and double out options .In section three,the pricing problems of rainbow barrier options are discussed using partial differential method.the pricing formulae of eight kinds of rainbow barrier options and four call-put parity are derived.In chapter 4,using remove singularity difference method and forward shooting target grid method respectively,the price of three kinds of modified barrier options:step options ,Parasian options and Parisian options are computed.In chapter 5,all work discussed above is concluded and further study directions are put forward.