美式期权定价问题罚函数法的欧拉-拉格朗日分裂格式

The Eulerian-Lagrangian Splitting Scheme in the Penalty Method for Solving the American Option Pricing

在求解多资产美式期权定价问题罚函数法的差分格式中首次引入欧拉-拉格朗日分裂技巧,使得在欧拉步中含罚函数项的方程可以准确求解,从而更好地解决了数值计算中期权值必须大于等于收益函数的问题.其次,在拉格朗日步中采用Crank-Nicholson格式,使得整体数值解的精度达到O(Δt2+h2).最后分别计算了单资产和多资产两个数值算例,数值结果均验证了新方法的有效性.

In this paper, the Eulerian-Lagrangian splitting skill is firstly employed in the difference scheme of penalty method for solving American multi-asset option pricing. In the step of Euler, the equation which includes the penalty term can be solved analytically, which is helpful to overcome the difficulty in keeping the value of option be positive. In the step of Lagrange, the C- N scheme is used, which improves the accuracy to O（Δt2 ＋ h2 ） . Two examples for both single- and multi-asset options are tested and the nu- merical results show the efficiency of the new method.