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Properties of Doubly Stochastic Poisson Process with affine intensity

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  • Alan De Genaro Dario
  • Adilson Simonis

Abstract

This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP) where the intensity process belongs to a class of affine diffusions. For any intensity process from this class we derive an analytical expression for probability distribution functions of the corresponding DSPP. A specification of our results is provided in a particular case where the intensity is given by one-dimensional Feller process and its parameters are estimated by Kalman filtering for high frequency transaction data.

Suggested Citation

  • Alan De Genaro Dario & Adilson Simonis, 2011. "Properties of Doubly Stochastic Poisson Process with affine intensity," Papers 1109.2884, arXiv.org, revised Sep 2011.
    • Handle: RePEc:arx:papers:1109.2884
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    References listed on IDEAS

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    1. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 297-302, October.
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    3. Dassios, Angelos & Jang, Jiwook, 2008. "The distribution of the interval between events of a Cox process with shot noise intensity," LSE Research Online Documents on Economics 31864, London School of Economics and Political Science, LSE Library.
    4. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," LSE Research Online Documents on Economics 16375, London School of Economics and Political Science, LSE Library.
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