一类美式股票期权定价的数值算法  

Numerical Algorithm of an American Stock Option Pricing

作　　者：薛婕 周圣武 江一鸣[1] Xue Jie;Zhou Shengwu;Jiang Yiming(School of Mathematical Sciences,Nankai University,Tianjin 300071,China;School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]南开大学数学科学学院,天津300071 [2]中国矿业大学数学学院,江苏徐州221116

出　　处：《南开大学学报（自然科学版）》2020年第4期1-7,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

摘　　要：基于Black-Scholes定价模型,建立了波动率服从GARCH(1,1)模型的一类美式看跌股票期权定价模型.采用跳格子有限差分法求解期权定价模型,并证明了跳格子差分格式是相容的、收敛的、稳定的.实证分析表明,与显式和隐式差分格式相比,跳格子差分格式是有效的.Based on the Black-Scholes pricing model,a kind of American stock put option pricing model which the volatility obbeys GARCH(1,1)model is established.It uses the Hopscotch finite difference method to solve option pricing equation and carries out empirical analysis.Comparing the result with Explicit and Implicit difference schemes,the effectiveness of the Hopscotch method is proved,and it is compatible,convergent and stable.

关 键 词：美式期权定价 GARCH(1 1)模型 跳格子法 

分 类 号：O211.6[理学—概率论与数理统计]