作　　者： ; ;

机构地区： 华南师范大学数学科学学院

出　　处： 《工程数学学报》 2010年第1期21-29,共9页

摘　　要： 本文研究三状态开关式波动率美式看跌期权的定价问题,假设波动率σ(t)取三个不同的值σ1,σ2,σ3,分别对应于股市中的熊市、振荡市和牛市,利用Δ对冲技巧得到了有三条自由边界(即最佳实施边界)的变分不等式模型;作为其应用,本文得到以下结果:若当前股票市场处于熊市(牛市),则在一定条件下,三状态开关式波动率美式看跌期权的最佳实施边界比标准美式看跌期权的最佳实施边界大(小),且三状态开关式波动率美式看跌期权的价格比标准美式看跌期权的价格低(高);若当前股票市场处于振荡市,则在一定条件下,三状态开关式波动率美式看跌期权的最佳实施边界比标准美式看跌期权的最佳实施边界小(大),且三状态开关式波动率美式看跌期权的价格比标准美式看跌期权的价格高(低)。 This paper discusses the fair price of American put options with three-state regime switching volatility. Assuming that the volatility σ（t） takes three different values σ1, σ2, σ3 which correspond to bearish, an oscillatory and a bullish stock market, respectively, and applying the △ hedging technique, we obtain a system of evolutionary variational inequalities which possesses three free boundaries （optimal exercise boundaries）. As an application, the following main results is obtained. The optimal exercise boundary of American put options with three-state regime switching volatility in the bearish （bullish） market is higher （smaller） than that of standard American put options and the price of American put options with three-state regime switching volatility in the bearish （bullish） market is smaller （higher） than that of standard American put options on some conditions. The optimal exercise boundary of American put options with three-state regime switching volatility in the oscillatory market is smaller （higher） than that of standard American put options and the price of American put options with three-state regime switching volatility in the oscillatory market is higher （smaller） than that of standard American put options on some conditions.

关 键 词： 开关式波动率 变分不等式 自由边界

领　　域： [理学] [理学]