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The Time Change Framework

In: Extreme Financial Risks and Asset Allocation

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  • Olivier Le Courtois
  • Christian Walter

Abstract

This chapter gives a detailed presentation of the time change framework introduced previously in Chapter 2, p. 22. The nature of time changes is recalled in the introduction. It is illustrated with a first example based on the Poisson process. The notion of subordination is then introduced and defined in full generality, before we can apply it to the time change of Brownian motion, in the case of a gamma clock. The situations where the daily variations of market activity are not independent — for instance when exchanged volumes display a certain degree of persistence — are modeled with a square root of time process…

Suggested Citation

  • Olivier Le Courtois & Christian Walter, 2014. "The Time Change Framework," World Scientific Book Chapters, in: Extreme Financial Risks and Asset Allocation, chapter 7, pages 147-180, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9781783263097_0007
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