Study On The Two Methods Of Fast Evaluating Of American Barrier Option

The study of barrier options has a long history.In the stochastic volatility model,the valuation of European option price and the problem of hedging mostly can be solved by some methods under the B-S model.The study of American barrier options pricing is a hot issue in the study of options.At present,scholars have gradually improved the research of European option pricing.There are many achievements in the study of American barrier options but most of them are studied by Monte Carlo simulation.This paper mainly studies the valuation and hedging of American barrier options,discusses the valuation and hedging strategy of American barrier options under stochastic volatility model and asset in asymmetry case,and investigate the valuation of American Parisian barrier options.On the condition that the underlying asset price is under certain distribution,the most basic form of the price symmetric relation(put-call symmetry)of the call and put option can be used to calculate the price of call option relating to put option[1].But in the study of stochastic volatility model,the asset price is not satisfied with this symmetry condition which lead to asymmetry of put-call.This article is in the condition that the asset price does not meet symmetry condition and uncorrelated relation between asset price process and volatility process in the stochastic volatility model,to study general self-duality theorem,valuation of American up&in and down&in option price and corresponding hedging strategies of contingent claims.The main conclusions of the discussion of self duality is as follow:theorem3,2.1 In the stochastic volatility model,the price of up&in American put barrier option with barrier level u,payoff function G(St)1?u?T time ?u can be calculated using following formula:(?)In addition,with only one barrier level is easy to be arbitraged by traders in the market.Therefore,the existence of Parisian options provides a hedge tool for market participants.In this paper,the valuation problem of American Parisian knock-out option is studied by LCT method.By introducing the excursion time variable I,the equation of time recovery value of the option has been derived and the valuation of the return value of option can be get.The results of down and out call option can be seen in theorem 4.2.1,theorem 4.2.2,theorem 4.2.3;the results of up and out put option can be seen in theorem 4.2.4.theorem 4.2.5.