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Well-balanced Lévy driven Ornstein–Uhlenbeck processes

Author

Listed:
  • Schnurr Alexander

    (Technische Universität Dortmund, Fakultät für Mathematik, LS IV, Dortmund, Deutschland)

  • Woerner Jeannette H. C.

Abstract

In this paper we introduce the well-balanced Lévy driven Ornstein–Uhlenbeck process as a moving average process of the form Xt = ∫ exp(-λ|t-u|)dLu. In contrast to Lévy driven Ornstein–Uhlenbeck processes the well-balanced form possesses continuous sample paths and an autocorrelation function which is decreasing not purely exponential but of the order λ|u|exp(-λ|u|). Furthermore, depending on the size of λ it allows both for positive and negative correlation of increments. We indicate how the well-balanced Ornstein–Uhlenbeck process might be used as mean or volatility process in semimartingale models.

Suggested Citation

  • Schnurr Alexander & Woerner Jeannette H. C., 2011. "Well-balanced Lévy driven Ornstein–Uhlenbeck processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 343-357, December.
    • Handle: RePEc:bpj:strimo:v:28:y:2011:i:4:p:343-357:n:4
    DOI: 10.1524/strm.2011.1089
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    References listed on IDEAS

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