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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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    1. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
    2. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    3. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
    4. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    5. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    6. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    8. Matthew P. S. Gander & David A. Stephens, 2007. "Simulation and inference for stochastic volatility models driven by Lévy processes," Biometrika, Biometrika Trust, vol. 94(3), pages 627-646.
    9. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    10. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    11. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    12. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    13. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    14. Hofert, Marius, 2011. "Efficiently sampling nested Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 57-70, January.
    15. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    16. Kyoung-Kuk Kim & Sojung Kim, 2016. "Simulation of Tempered Stable Lévy Bridges and Its Applications," Operations Research, INFORMS, vol. 64(2), pages 495-509, April.
    17. Ole E. Barndorff‐Nielsen & Neil Shephard, 2003. "Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295, June.
    18. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    19. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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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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