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Some Further Results on the Tempered Multistable Approach

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  • Olivier Courtois

    (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 Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(2), pages 87-109, June.
    • Handle: RePEc:kap:apfinm:v:25:y:2018:i:2:d:10.1007_s10690-018-9240-y
    DOI: 10.1007/s10690-018-9240-y
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    References listed on IDEAS

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    1. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
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    3. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    4. Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, vol. 181(1), pages 53-63.
    5. 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..
    6. Olivier Le Courtois & Christian Walter, 2014. "The Computation of Risk Budgets under the Lévy Process Assumption," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 87-108.
    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.
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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.
    2. Silvia Faroni & Olivier Le Courtois & Krzysztof Ostaszewski, 2022. "Equivalent Risk Indicators : VaR, TCE, and Beyond," Post-Print hal-04325627, HAL.

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