High Precision Difference Method Of Option Pricing Model

In recent years, with the development of fnancial market option has becomeone of the most active in the fnancial market of fnancial derivatives.Because ofits superior function and fexibility, diversity and other characteristics,So it getsrapid development and application.Option pricing theory is considered as one ofthe most successful fnancial theory,it is also be regarded as the only one beforepractice theory in fnancial economics, the option pricing problem is the coreissue of study options.The preface of the article expounds the option pricing theory and its impor-tance in the feld of fnancial market and fnance. This paper briefy introducesthe option of superior function, type and option theory in fnance position, Dis-cusses several important methods of fnancial derivatives pricing, the focus of thestudy option theory and good results has made by option pricing.The second part reviews the history of the option pricing theory.No riskhedge principle are introduced in the process of Black-Scholes diferential equa-tion deriving,the derivation process of the pricing formula is introduced in detail,the main research work presented in this paper is instructed.The third part mainly introduced the compact diference method of optionpricing model.Frist option pricing model of backward problem is transformedinto a positive problem. By using the diferential equation of derivative rela-tions handling truncation error term,high order compact diference scheme isobtained.At the same time, the article analyzed the stability of the diferenceschemes.Through the numerical experiments show that diference scheme hasreached the second order convergence.The fourth part introduces a compact diference method with non-uniformto solve option pricing model. Because the payment function is not smooth at thestrike price, the fourth-order diference scheme can achieve two order on uniformgrid when it is calculated,So grid stretching transformation is used in this part, encrypting grid node around the strike price, then equidistant grid becomesnon-equidistant grid, thereby the error of option value is reduced in around thestrike price. Numerical experiments show that this method is efective, makingthe diference scheme to fourth order concergence speed as a whole.At last thisarticle has carried on the summary.