The Use of Numeraires in Multi-Dimensional Black-Scholes Partial Differential Equations

Abstract

计价单位变换在期权定价问题的计算上给了很重要的简单化。用这个方法可以减少要考虑的风险源个数，于是它在具有多个风险源复杂的衍生证券定价上很有用。在这篇文章中，我们在 PDE 理论观点之下研究计价单位方法的数学理论并且举 5 个典型而具体的例子来说明它。在 PDE 理论观点上，计价单位方法是个减少 PDE 被定义的区域维数的方法.The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that have several sources of risks. In this article, we considered the underlying mathematical theory of numeraire technique in the viewpoint of PED theory and illustrated it with five concrete pricing problems. In the viewpoint of PED theory, the numeraire technique is a method of reducing the dimension of status spaces where PDE is defined.