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Some properties of the one-dimensional subordinated stable model

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  • Panov, Vladimir

Abstract

In this paper, we consider some properties of the model constructed from the one-dimensional stable processes by changing the time to a non-decreasing Lévy process. Our first result reveals a relation between this class of processes and the class of time-changed Brownian motions. Moreover, we describe the CGMY (Carr–Geman–Madan–Yor) model as subordinated stable process, and show the representation of the Lévy density of the corresponding subordinator via the Mellin–Barnes integral.

Suggested Citation

  • Panov, Vladimir, 2019. "Some properties of the one-dimensional subordinated stable model," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 80-84.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:80-84
    DOI: 10.1016/j.spl.2018.11.002
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    References listed on IDEAS

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    1. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    3. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
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