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Some Further Results on the Tempered Multistable Approach

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  • Olivier Le Courtois

    (EM - EMLyon Business School)

Abstract

This article provides new results on the tempered multistable approach. After a preliminary section recalling the main definitions, we show the correspondence between a series representation and a characteristic function representation for asymmetrical field-based tempered multistable processes and for asymmetrical independent increments tempered multistable processes. We also show that both processes are semimartingales, which is a convenient property in finance. Next, we study the structure of autocorrelations that is conveyed by this approach. Finally, we provide an illustration showing the term structures of Value-at-Risk that can be obtained with this model.

Suggested Citation

  • Olivier Le Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Post-Print hal-02312142, HAL.
    • Handle: RePEc:hal:journl:hal-02312142
    DOI: 10.1007/s10690-018-9240-y
    Note: View the original document on HAL open archive server: https://hal.science/hal-02312142
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    References listed on IDEAS

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    1. Ronan Le Guével & Jacques Lévy Véhel & Lining Liu, 2015. "On Two Multistable Extensions of Stable Lévy Motion and Their Semi-martingale Representations," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1125-1144, September.
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    4. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    5. K. J. Falconer & J. Lévy Véhel, 2009. "Multifractional, Multistable, and Other Processes with Prescribed Local Form," Journal of Theoretical Probability, Springer, vol. 22(2), pages 375-401, June.
    6. Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, vol. 181(1), pages 53-63.
    7. 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..
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    Cited by:

    1. Silvia Faroni & Olivier Le Courtois & Krzysztof Ostaszewski, 2022. "Equivalent Risk Indicators: VaR, TCE, and Beyond," Risks, MDPI, vol. 10(8), pages 1-19, July.

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