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Random variate generation for exponential and gamma tilted stable distributions

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

Abstract

We develop a new efficient simulation scheme for sampling two families of tilted stable distributions: exponential tilted stable (ETS) and gamma tilted stable (GTS) distributions. Our scheme is based on two-dimensional single rejection. For the ETS family, its complexity is uniformly bounded over all ranges of parameters. This new algorithm outperforms all existing schemes. In particular, it is more efficient than the well-known double rejection scheme, which is the only algorithm with uniformly bounded complexity that we can find in the current literature. Beside the ETS family, our scheme is also flexible to be further extended for generating the GTS family, which cannot easily be done by extending the double rejection scheme. Our algorithms are straightforward to implement, and numerical experiments and tests are conducted to demonstrate the accuracy and efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:108593
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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.

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    More about this item

    Keywords

    exponentially tilted stable distribution; gamma tilted stable distribution; exact Simulation Algorithms; Monte Carlo simulation; random variate generation; two-dimensional single rejection; tempered stable distribution; Lévy process;
    All these keywords.

    JEL classification:

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

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