Study On Pricing For Asian Option Based On The Homotopy Analysis Method

Asian options pricing is one of the important issues of the study on the pricingof financial derivatives assets,and the geometric average Asian options has displayedits pricing formula.Because the arithmetic average Asian options are not subject tothe normal distribution which is particularity.There is no analytical solution for itspricing equation up to now.Therefore,For pricing arithmetic average Asian options isa research question.This paper mostly studied the pricing of the Asian options by using the homotopyanalysis method in the case of complete financial market,This report consists fourchapters.In the first chapter,We introduce the conception of options and its developinghistory,and the Black-scholes pricing model.And We introduce the basic idea of thehomotopy analysis method.In the second chapter,We deduced the Asian options pricing model,And thendeduce the arithmetic average Asian options pricing model and make some homo-topy deformation,Convert it to a second order partial diferential equation with freeboundary,finally, constructed a homotopy equation in accordance with its financialimplications, Success to make the free boundary problem into multiple fixed boundaryproblem.In the third chapter,Before solving the equation,We analyze the convergence ofthe zero order and high order deformation equation,And given the rationality of themethod.