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Efficient simulation of Lévy-driven point processes

  • Yan Qu (a1), Angelos Dassios (a1) and Hongbiao Zhao (a2)

Abstract

In this paper, we introduce a new large family of Lévy-driven point processes with (and without) contagion, by generalising the classical self-exciting Hawkes process and doubly stochastic Poisson processes with non-Gaussian Lévy-driven Ornstein–Uhlenbeck-type intensities. The resulting framework may possess many desirable features such as skewness, leptokurtosis, mean-reverting dynamics, and more importantly, the ‘contagion’ or feedback effects, which could be very useful for modelling event arrivals in finance, economics, insurance, and many other fields. We characterise the distributional properties of this new class of point processes and develop an efficient sampling method for generating sample paths exactly. Our simulation scheme is mainly based on the distributional decomposition of the point process and its intensity process. Extensive numerical implementations and tests are reported to demonstrate the accuracy and effectiveness of our scheme. Moreover, we use portfolio risk management as an example to show the applicability and flexibility of our algorithms.

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Corresponding author

*Postal address: Department of Statistics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK.
**Postal address: School of Statistics and Management, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai 200433, China; Shanghai Institute of International Finance and Economics, 777 Guoding Road, Shanghai 200433, China.

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Efficient simulation of Lévy-driven point processes

  • Yan Qu (a1), Angelos Dassios (a1) and Hongbiao Zhao (a2)

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