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Superposition of COGARCH processes

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  • Behme, Anita
  • Chong, Carsten
  • Klüppelberg, Claudia

Abstract

We suggest three superpositions of COGARCH (sup-CO-GARCH) volatility processes driven by Lévy processes or Lévy bases. We investigate second-order properties, jump behaviour, and prove that they exhibit Pareto-like tails. Corresponding price processes are defined and studied. We find that the sup-CO-GARCH models allow for more flexible autocovariance structures than the COGARCH. Moreover, in contrast to most financial volatility models, the sup-CO-GARCH processes do not exhibit a deterministic relationship between price and volatility jumps. Furthermore, in one sup-CO-GARCH model not all volatility jumps entail a price jump, while in another sup-CO-GARCH model not all price jumps necessarily lead to volatility jumps.

Suggested Citation

  • Behme, Anita & Chong, Carsten & Klüppelberg, Claudia, 2015. "Superposition of COGARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1426-1469.
  • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1426-1469
    DOI: 10.1016/j.spa.2014.11.004
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    References listed on IDEAS

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