Black-Scholes期权定价模型的五点式混合差分方法  

Five-Point Form Hybrid Difference Method for Black-Scholes Option Pricing Model

作　　者：蹇明[1] 宜娜[1] 张春晓[1] 

机构地区：[1]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《经济数学》2011年第4期66-70,共5页Journal of Quantitative Economics

基　　金：中央高校基本科研业务费专项资金资助(2011TS033)

摘　　要：研究了欧式看涨期权定价问题的差分方法,将Black-Scholes方程等价代换为标准抛物型偏微分方程,在时间方向上采用前、后差商,空间方向上采用五点差分格式,再引入参数θ建立一个稳定的混合差分格式.根据Von Neumann条件证明了该格式的稳定性及收敛性,并通过数值计算的实际应用,结果表明该算法适用于到期日较长的期权定价.We studied the difference method for the European Call option pricing problem. Firstly we equivalently trans- formed the Blaek-Seholes equation into a standard parabolic partial differential equation. We adopted forward difference and backward differenee with respect to the direetion of time. Meanwhile, we adopted five-point difference scheme with respect to the direction of spaee. Next, we used the parameter 0 to establish a hybrid difference scheme whieh is stable. Moreover, according to Von Neumann condition we proved the stability and convergence of this scheme. Finally, we show that the method is applicable to long term option pricing problem through the result of numerieal experiments.

关 键 词：期权定价 数值方法 BLACK-SCHOLES模型 

分 类 号：O211.63[理学—概率论与数理统计]