美式看涨期权的最优实施边界公式推导及模拟

文章研究了美式看涨期权的最优实施边界问题.对美式看涨期权的最优实施边界满足的非线性第二类Volterra积分方程进行了详细推导,并对最优实施边界提出复合梯形格式.通过数值试验分析得出复合梯形格式得到的数值解符合最优实施边界性质,同时也通过MATLAB编程模拟出最优实施边界在初始点的值及整个期限内的最优实施边界图,对模拟结果进行了经济学解释.

The Derivation and Simulation about the Formula for the Optimal Exercise Boundary of American Call Option

To focuses on a question about optimal exercise boundary of the American call option.We derive a second category and the non-linear Volterra integral equation which is satisfied by American call option,and propose a composite trapezoid scheme about optimal exercise boundary.Based on the numerical scheme of the optimal exercise boundary,the experimental analysis shows that the numerical solution of the boundary is consistent with the nature of the optimal exercise boundary.In the following,we simulate the value of optimal exercise boundary at the initial point and give a boundary map about the whole period of the optimal exercise boundary through MATLAB program.A last,an economic interpretation about the simulation results is shown.