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Exact simulation for a class of tempered stable

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  • Dassios, Angelos
  • Qu, Yan
  • Zhao, Hongbiao

Abstract

In this paper, we develop a new scheme of exact simulation for a class of tempered stable (TS) and other related distributions with similar Laplace transforms. We discover some interesting integral representations for the underlying density functions that imply a unique simulation framework based on a backward recursive procedure. Therefore, the foundation of this simulation design is very different from existing schemes in the literature. It works pretty efficiently for some subclasses of TS distributions, where even the conventional acceptancerejection mechanism can be avoided. It can also generate some other distributions beyond the TS family. For applications, this scheme could be easily adopted to generate a variety of TSconstructed random variables and TS-driven stochastic processes for modelling observational series in practice. Numerical experiments and tests are performed to demonstrate the accuracy and effectiveness of our scheme

Suggested Citation

  • Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:86981
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    File URL: http://eprints.lse.ac.uk/86981/
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    Cited by:

    1. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    2. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "Correlating L\'evy processes with Self-Decomposability: Applications to Energy Markets," Papers 2004.04048, arXiv.org, revised Jul 2020.
    3. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Monte Carlo simulation; Exact simulation; Backward recursive scheme; Stable distribution; Tempered stable distribution; Exponentially tilted stable distribution; Lévy process; Lévy subordinator; Leptokurtosis;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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