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Fractional Lévy Cox–Ingersoll–Ross and Jacobi processes

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  • Fink, Holger
  • Schlüchtermann, Georg

Abstract

We prove a general Picard–Lindelöf-type framework for stochastic differential equations driven by Mandelbrot–Van Ness fractional Lévy processes. This allows us to derive the existence of a fractional Lévy Cox–Ingersoll–Ross and Jacobi model with almost surely positive, respectively bounded, samples paths.

Suggested Citation

  • Fink, Holger & Schlüchtermann, Georg, 2018. "Fractional Lévy Cox–Ingersoll–Ross and Jacobi processes," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 84-91.
    • Handle: RePEc:eee:stapro:v:142:y:2018:i:c:p:84-91
    DOI: 10.1016/j.spl.2018.07.004
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    References listed on IDEAS

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    1. Holger Fink, 2016. "Conditional Distributions of Mandelbrot–van ness Fractional LÉVY Processes and Continuous-Time ARMA–GARCH-Type Models with Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 30-45, January.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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