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A stochastic processes toolkit for risk management: Mean reverting processes and jumps

Author

Listed:
  • Brigo, Damiano

    (Fitch Solutions, 101 Finsbury Pavement, London EC2A 1RS, UK)

  • Dalessandro, Antonio
  • Neugebauer, Matthias
  • Triki, Fares

Abstract

In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. this paper aims to introduce a number of different stochastic processes that can help in grasping the essential features of risk factors, describing different asset classes or behaviours. the paper does not aim to be exhaustive, but gives examples and a feeling for practically implementable models, allowing for stylised features in the data. these models can also be used as building blocks to build more complex models, although, for a number of risk management applications, the models developed here suffice for the first step in the quantitative analysis. the broad qualitative features addressed here are fat tails and mean reversion. the introduction, the general framework and fat tails have been addressed in the authors’ paper published in vol. 2, no. 4 of the journal. this paper deals with mean reversion both on its own and jointly with fat tails.

Suggested Citation

  • Brigo, Damiano & Dalessandro, Antonio & Neugebauer, Matthias & Triki, Fares, 2010. "A stochastic processes toolkit for risk management: Mean reverting processes and jumps," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 3(1), pages 65-83, January.
    • Handle: RePEc:aza:rmfi00:y:2010:v:3:i:1:p:65-83
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    More about this item

    Keywords

    risk management; stochastic processes; risk factors; fat tails; mean reversion; jump diffusion processes; variance gamma processes;
    All these keywords.

    JEL classification:

    • G2 - Financial Economics - - Financial Institutions and Services
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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