Research On Two Problems Of Asia Option Pricing

In the financial market, path-dependent option is more competitive than standardoption profit from its path-dependent character, and increasingly become the researcher'sfocus of the option pricing field. CEV model is the generalization of the Geometric Brown-ian motion, the option pricing research under CEV process mainly focuses on lookbackoptions and barrier options, but ignores the Asian options which is also path-dependent.In this paper we consider two problems on Asian option pricing: pricing geometricAsian option on underlying assets obeying CEV process; pricing arithmetic average Asianoption with ?oating strike price under B-S model.Firstly, standard geometric Asian option and its pricing model are considered, thenCEV is introduced. By virtue of the technique Phelim P.Boyle and Yisong Tian usedto price lookback options and barrier options under CEV process, the application of abinomial tree is put forward to get the price of the geometric Asian option with discretedividend paid under CEV process. Besides, we extend the geometric average weightnumber to the more commonly weighted geometric average.Secondly, we consider the pricing of the arithmetic average Asian option with ?oatingstrike price under B-S model. In order to simplify the fussy computation in the binomialtree method, we introduce the Parabolic interpolation on the basis of the existed linearinterpolation. By the combine of the binomial tree method and the Parabolic interpo-lation, we obtained the approximate price of the arithmetic average Asian option with?oating strike price. In the end, we present the instance analysis, validate the validityand astringency of the binomial tree method, at the same time proved that the parabolicinterpolation is more e?cient than the linear interpolation.