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Equivalent martingale measures for Lévy-driven moving averages and related processes

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  • Basse-O’Connor, Andreas
  • Nielsen, Mikkel Slot
  • Pedersen, Jan

Abstract

In the present paper we obtain sufficient conditions for the existence of equivalent local martingale measures for Lévy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions, also necessary. For instance, this is the case for moving averages driven by an α-stable Lévy process with α∈(1,2].

Suggested Citation

  • Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan, 2018. "Equivalent martingale measures for Lévy-driven moving averages and related processes," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2538-2556.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:8:p:2538-2556
    DOI: 10.1016/j.spa.2017.09.022
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    References listed on IDEAS

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    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    2. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    3. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
    4. Cheridito, Patrick, 2004. "Gaussian moving averages, semimartingales and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 47-68, January.
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