Effect of basis functions in Least-Squares Monte Carlo (LSM) for pricing options.

摘要

In modern financial world, it is one of the most challenging problems to valuate American-style options. Finite difference methods could be used only if the dimensions of derivatives are no more than three. In order to overcome the restriction, a simple and powerful approach, known as Least-Squares Monte Carlo(LSM), appeared in our sight, which was firstly proposed by Longstaff & Schwartz (2001).This approach is really easy to implement, because only simple least-squares is essentially required. Besides, it could be widely applied to more complex and general options, and LSM has its advantage of dimensional insensitiveness.;Nowadays, the Least-Squares Monte Carlo (LSM) approach has definitely become a powerful method for pricing options. This backward method considerably supports the growing interest in financial models that involve multiple assets, in these situations, traditional finite difference method fades certainly. However, one would face an important and hard choice in the step of regression by using Least-Squares Monte Carlo (LSM), which in fact, is the choice of basis functions.;This paper aims at the effect of different basis functions in high-dimensional cases for pricing American and European options. Particularly, for European options, a flexible method with PDE is applied to better analyze the accuracy of numerical results depending on explicit solutions. Hopefully and believably, the statements in this paper would provide guiding significance.