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Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance

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  • Martin Keller-Ressel
  • Claus Griessler
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    Abstract

    We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance dominates its quadratic variation in increasing convex order. The results have immediate applications to the pricing of options on realized variance. For a class of models including time-changed Levy models and Sato processes with symmetric jumps our results show that options on variance are typically underpriced, if quadratic variation is substituted for the discretely sampled realized variance.

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    File URL: http://arxiv.org/pdf/1103.2310
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1103.2310.

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    Date of creation: Mar 2011
    Date of revision: Oct 2012
    Handle: RePEc:arx:papers:1103.2310

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    Web page: http://arxiv.org/

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