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Characteristic function of time-inhomogeneous Lévy-driven Ornstein–Uhlenbeck processes

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  • Vrins, Frédéric

Abstract

We derive the characteristic function (CF) of integrals of Lévy-driven Ornstein–Uhlenbeck processes with time-inhomogeneous coefficients. The resulting expression takes the form of the exponential integral of the time-changed characteristic exponent. This result is applied to some examples leading to closed form expressions. In particular, it drastically simplifies the calculations of the CF of integrated Compound Poisson processes compared to the standard approach relying on joint conditioning on inter-arrival jump times.

Suggested Citation

  • Vrins, Frédéric, 2016. "Characteristic function of time-inhomogeneous Lévy-driven Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 55-61.
    • Handle: RePEc:eee:stapro:v:116:y:2016:i:c:p:55-61
    DOI: 10.1016/j.spl.2016.04.013
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    References listed on IDEAS

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    1. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    2. 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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