Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 95

The Cayley Transform refers to a group of related concepts. The relevance to our work is that it appears when proving the stability of finite difference schemes for two-factor option pricing problems as we shall discuss in Chapters 18, 22 and 23. It has been applied in fixed-income pricing as discussed in Davidson and Levin (2014).

In general, we define:

(5.22)

In the case where A is positive definite, we can compute the norm of Q as follows:

This result was proved in Kellogg (1964), and it is an important lemma to prove unconditional stability of splitting schemes. In the same way it is possible to show that .