Volume 47, pp. 57-72, 2017.

Incremental computation of block triangular matrix exponentials with application to option pricing

Daniel Kressner, Robert Luce, and Francesco Statti

Abstract

We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomial diffusion models. In this setting, a discretization process produces a sequence of nested block triangular matrices, and their exponentials are to be computed at each stage until a dynamically evaluated criterion allows to stop. Our algorithm is based on scaling and squaring. By carefully reusing certain intermediate quantities from one step to the next, we can efficiently compute such a sequence of matrix exponentials.

Full Text (PDF) [358 KB]

Key words

matrix exponential, block triangular matrix, polynomial diffusion models, option pricing

AMS subject classifications

15A16, 65F60, 91G20

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