基于牛顿法的美式期权最优实施边界的数值模拟

摘要

The optimal exercise boundary of American put options is characterized by monotone non -decreasing and convexity .To seek for the best numerical solution conformed to the properties , New-ton’ s iteration method is proposed in this paper to solve the nonlinear optimal boundary problem . The numerical tests show that the graphs of composite trapezoid scheme by Newton ’ s iteration meth-od conform to the properties of the optimal exercise boundary .Compared with the composite trape-zoid scheme by fixed-point iteration method , it is finally concluded that there are slight errors be-tween these two numerical schemes for solving the optimal exercise boundary .%美式看跌期权最优实施边界具有单调非减和凸性质，为寻找符合性质的数值解法，本文对非线性最优实施边界问题提出了牛顿迭代格式。通过数值试验分析得出牛顿迭代法下复合梯形格式的图形符合最优实施边界性质，并与不动点迭代法下的复合梯形格式求解的最优实施边界进行了比较，得到两种方法求解的最优实施边界数值解误差非常小。