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Maximum likelihood estimation for Wishart processes

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  • Alfonsi, Aurélien
  • Kebaier, Ahmed
  • Rey, Clément

Abstract

In the last decade, there has been a growing interest to use Wishart processes for modeling, especially for financial applications. However, there are still few studies on the estimation of its parameters. Here, we study the Maximum Likelihood Estimator (MLE) in order to estimate the drift parameters of a Wishart process. We obtain precise convergence rates and limits for this estimator in the ergodic case and in some nonergodic cases. We check that the MLE achieves the optimal convergence rate in each case. Motivated by this study, we also present new results on the Laplace transform that extend the recent findings of Gnoatto and Grasselli (2014) and are of independent interest.

Suggested Citation

  • Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:11:p:3243-3282
    DOI: 10.1016/j.spa.2016.04.026
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    Cited by:

    1. Gaetano Bua & Daniele Marazzina, 2021. "On the application of Wishart process to the pricing of equity derivatives: the multi-asset case," Computational Management Science, Springer, vol. 18(2), pages 149-176, June.
    2. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    3. Aur'elien Alfonsi & David Krief & Peter Tankov, 2018. "Long-time large deviations for the multi-asset Wishart stochastic volatility model and option pricing," Papers 1806.06883, arXiv.org.

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