Superposition of COGARCH processes

Anita Behme, Carsten Chong and Claudia Klüppelberg

Stochastic Processes and their Applications, 2015, vol. 125, issue 4, 1426-1469

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.

Keywords: COGARCH; Continuous-time GARCH model; Independently scattered; Infinite divisibility; Lévy basis; Lévy process; Random measure; Stationarity; Stochastic volatility process; Sup-CO-GARCH; Superposition (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:4:p:1426-1469

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DOI: 10.1016/j.spa.2014.11.004

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