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Markov cubature rules for polynomial processes

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  • Filipović, Damir
  • Larsson, Martin
  • Pulido, Sergio

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 such rules using algebraic techniques. Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial processes.

Suggested Citation

  • Filipović, Damir & Larsson, Martin & Pulido, Sergio, 2020. "Markov cubature rules for polynomial processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1947-1971.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:1947-1971
    DOI: 10.1016/j.spa.2019.06.010
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    References listed on IDEAS

    as
    1. Damir Filipovic & Damien Ackerer & Sergio Pulido, 2018. "The Jacobi Stochastic Volatility Model," Post-Print hal-01338330, HAL.
    2. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    3. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    4. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    5. Hao Zhou, 2003. "Itô Conditional Moment Generator and the Estimation of Short-Rate Processes," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 250-271.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    7. Francesca Biagini & Yinglin Zhang, 2016. "Polynomial Diffusion Models for Life Insurance Liabilities," Papers 1602.07910, arXiv.org, revised Sep 2016.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    9. Damir Filipovic & Martin Larsson & Tony Ware, 2017. "Polynomial processes for power prices," Papers 1710.10293, arXiv.org, revised Apr 2018.
    10. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
    11. Biagini, Francesca & Zhang, Yinglin, 2016. "Polynomial diffusion models for life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 114-129.
    12. Christa Cuchiero & Martin Keller-Ressel & Josef Teichmann, 2012. "Polynomial processes and their applications to mathematical finance," Finance and Stochastics, Springer, vol. 16(4), pages 711-740, October.
    13. Damien Ackerer & Damir Filipović & Sergio Pulido, 2018. "The Jacobi stochastic volatility model," Finance and Stochastics, Springer, vol. 22(3), pages 667-700, July.
    14. Damir Filipović & Martin Larsson & Tony Ware, 2018. "Polynomial Processes for Power Prices," Swiss Finance Institute Research Paper Series 18-34, Swiss Finance Institute.
    15. Cuchiero, Christa, 2019. "Polynomial processes in stochastic portfolio theory," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1829-1872.
    16. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
    17. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    18. Kristian Stegenborg Larsen & Michael Sørensen, 2007. "Diffusion Models For Exchange Rates In A Target Zone," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 285-306, April.
    19. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
    20. Damir Filipović & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Swiss Finance Institute Research Paper Series 17-60, Swiss Finance Institute.
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    Cited by:

    1. Qi Feng & Jianfeng Zhang, 2021. "Cubature Method for Stochastic Volterra Integral Equations," Papers 2110.12853, arXiv.org, revised Jul 2023.

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