基于最小二乘法的美式期权定价的最优停时分析

An Analysis for Optimal Stopping of American Option Pricing Based on a Least Squares Regression

给出一种基于最小二乘法的美式期权定价的最优停时的数值算法。首先通过构造一个函数的有限集替代动态规划中的条件期望 ,其次使用蒙特卡洛模拟和最小二乘法计算第一步中的值函数。最后 ,在一般意义下 ,证明该算法的收敛性。

This paper gives an numerical algorithm for optimal stopping of American option prices, based on least squares regression. First, in this algorithm, the condition expectation in the dynamic programming principle is replaced by projections on a finite set of functions. Secondly, it uses Monte-Carlo Simulations and least squares regression to compute the value function of the first one. Finally, its general convergence is proved.