One Fast Numerical Method Of American Option Pricing

Option is one kind of financial derivatives people designed to avoid the marketrisk.Option pricing is the core question of theory research and practical applicationof financial derivatives.The option pricing is a frontier problem as well as hot issueof financial engineering and financial mathematics at present.As a derivative produc-t,option's pricing model depends on the evolution of the asset. In the continuous timecase,the evolution of asset price can be described by a stochastic differential equa-tion,and as its derivatives,option's pricing is for a given solution of partial differentialequations. Therefore,we can use the theory and methods of the partial differential e-quations to establish various mathematical option pricing models,derive the optionpricing formula,analysis the option's pricing structure in depth,use numerical methodto solve the partial differential equations and get the price.For American options canbe exercised at any time up to the maturity dates,they are more flexibility in prac-tice.However,no closed-form solutions exist for American options of their valuationin general case.Therefore it is important to study the numerical methods for Americanoption pricing.In this paper,we propose a new numerical method for American option pric-ing.The main content of the thesis is presented as follows:In chapter one,we briefly introduce some basic option knowledge,the American op-tion pricing model and the property of American option price.In chapter tow, we Introduces a unbounded area of heat conduction equations on thenumerical method.We first introduce a artificial boundary conditions,and then in-troduce a accurate artificial boundary conditions make the original problem into alimited area of the thermal conductivity equations.So the finite difference method canbe used to solve the problem of limited the calculation area.In chapter three,we present the method of line. In chapter four through the artificial boundary method to solve the semi-infinite area ad Black-Scholes boundary conditions, With more and more free boundary method forquickly solve a d American options pricing problem.