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Markov Cubature Rules for Polynomial Processes

Author

Listed:
  • Damir Filipović

    (Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute)

  • Martin Larsson

    (ETH Zurich)

  • Sergio Pulido

    (Université d' Évry-Val-d'Essonne)

Abstract

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study the existence of such rules using algebraic techniques. These rules aim to improve the tractability and ease the implementation of models where the underlying factors are polynomial processes.

Suggested Citation

  • Damir Filipović & Martin Larsson & Sergio Pulido, 2016. "Markov Cubature Rules for Polynomial Processes," Swiss Finance Institute Research Paper Series 16-79, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1679
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2890002
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    Cited by:

    1. Giorgia Callegaro & Lucio Fiorin & Andrea Pallavicini, 2021. "Quantization goes polynomial," Quantitative Finance, Taylor & Francis Journals, vol. 21(3), pages 361-376, March.

    More about this item

    Keywords

    Polynomial Process; Cubature Rule; Asymptotic Moments; Transition Rate Matrix; Transition Probabilities; Negative Probabilities;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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