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

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  • Daniel Kressner
  • Robert Luce
  • 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.

Suggested Citation

  • Daniel Kressner & Robert Luce & Francesco Statti, 2017. "Incremental computation of block triangular matrix exponentials with application to option pricing," Papers 1703.00182, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1703.00182
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    1. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
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    Cited by:

    1. Damir Filipovi'c & Kathrin Glau & Yuji Nakatsukasa & Francesco Statti, 2019. "Weighted Monte Carlo with least squares and randomized extended Kaczmarz for option pricing," Papers 1910.07241, arXiv.org.
    2. Al Mugahwi, Mohammed & De La Cruz Cabrera, Omar & Fenu, Caterina & Reichel, Lothar & Rodriguez, Giuseppe, 2021. "Block matrix models for dynamic networks," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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