Two Methods For The Valuation Of American Call Options With Continuous Dividend

This paper mainly studies the option pricing problem.As the financial derivative market is booming worldwide,there are more extensive and deep-going studies on option,an important part of financial derivative instruments.Currently,the studies can be divided into two parts: option pricing and option trading strategy.Since whether the option trading strategy is suitable or not depends on its pricing,this paper is mainly on the valuation of options.As the equation for optimal exercise boundary of American option cannot be demonstrated by the explicit expression of elementary function,it’s rather difficult to price it.This article,however,based on Black-Scholes,an equation on American option pricing theory,proposes a new method in numerical option pricing and analyzing approximation.These two ways can precisely locate the optimal exercise boundary and make the accurate pricing of American options possible.Firstly,a new type of predictor-corrector format is developed.This format is an effective solution to the valuation of American call options with continuous dividend.Predictor format and corrector format are respectively established according to Black-Scholes equation,boundary value condition,initial value condition and optimal exercise boundary condition.The alternate use of predictor and corrector formula leads to the discrete data of optimal exercise boundary and option price.Through numerical experiment,we verify the effectiveness,convergence and sustainability of the format and calculate its accuracy and efficiency.It’s proved that our format can fully meet the actual need of option application.Secondly,a new type of analyzing approximation is developed by using the homotopy analysis method.This approach is effective in providing analyzing approximation formula for optimal exercise boundary of American call options with continuous dividend,and its convergence,effectiveness,sustainability and comparatively high accuracy have already been proved by mathematical experiments.As the equation is analytical,it is effective at anytime in option duration and is more convenient compared with those numerical ones.The greatest advantage lies in the fact that we only need to calculate for one time and can directly use the equation when facing the same option.Such a concise and effective formula,to our knowledge,is the first to come in valuating American call options with continuous dividend.