Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium
分析美式看跌期权分解为欧式期权加提前行权溢价的数值实现，提出一种基于该分解和Richardson外推的新算法，通过修正离散时间提前行权溢价使其单调收敛，并用牛顿法快速计算最优行权边界，数值实验表明该算法准确、高效且易于实现。
This paper presents a detailed analysis of the numerical implementation of the American put option decomposition into an equivalent European option plus an early exercise premium (Kim 1990, Jacka 1991, Carr et al. 1992). It subsequently introduces a new algorithm based upon this decomposition and Richardson extrapolation. This new algorithm is based upon (a) the derivation of the correct order for the error term when applying Richardson extrapolation, which is used to control the error of the extrapolated prices, (b) an innovative adjustment of Kim's (1990) discrete-time early exercise premium, so that these premiums monotonically converge and, therefore, it is appropriate to use them in extrapolation, and (c) the optimal exercise frontier can be quickly computed through Newton's method, permitting the efficient implementation of the decomposition formula in practice. Numerical experiments show that this new algorithm is accurate, efficient, easy to implement, and competitive in comparison with other methods. Finally, it can also be applied to other American exotic securities.