美式期权的Black-Scholes的定价方法及鞅  

Black-scholes of american option pricing method and martingale analysis

作　　者：郭园园[1] 王永茂[1] 路秀玲[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第11期1576-1579,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：河北省教育厅基金资助项目(Z2008136)

摘　　要：为求解违约时间为无穷大时美式期权的执行价格.结合期权执行时间服从布朗运动的特点,对期权执行时间进行了鞅分析,并求出停时价格为确定值时的概率,通过鞅方法对B-S微分方程求解,得出基于鞅的期权价格;通过期权定价的随机波动的概率密度分布,依个人情况选择在可承受范围内的最大值(看涨)和最小值(看跌),当最大、最小值确定时,将欧式期权的价格与可承受风险综合考虑,得出美式期权的预测价格.对风险系数偏爱不同的投资者有直接的参考作用.To solve the execution price of American option when the breach time to infinity, this study first combined with that the option exercise obeys the Brown motion characteristics, carried out the martingale analysis over the option execution time, and calculated the probability of the stop price order at a given price, then by solving the B-S differential equation with martingale approach, obtained the option prices. Through the distribution of the probability density of the random fluctuations of option pricing, according to personal situation that can withstand within the maximum(call option) and minimum(put option), and considering that when the maximum and minimum values were determined, the price of the European option put with risk tolerance take into account, this study drawn the forecast prices of American option. The result provides direct reference for investors with difference risk coefficient preferences.

关 键 词：期权定价 布朗运动 鞅方法 BLACK-SCHOLES公式 美式期权 随机波动 风险系数 停时 

分 类 号：F830.9[经济管理—金融学]