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A Short Rate Model Using Ambit Processes

  • José Manuel CorcueraEmail author
  • Gergely Farkas
  • Wim Schoutens
  • Esko Valkeila
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

In this article, we study a bond market where short rates evolve as
$$r_{t} =\displaystyle\int _{ -\infty }^{t}g(t - s)\sigma _{ s}W(\mathrm{d}s)$$
where \(g : (0,\infty ) \rightarrow \mathcal{R}\) is deterministic, σ ≥ 0 is also deterministic, and W is the stochastic Wiener measure. Processes of this type are also called Brownian semistationary processes and they are particular cases of ambit processes. These processes are, in general, not of the semimartingale kind. We also study a fractional version of the Cox–Ingersoll–Ross model. Some calibration and simulations are also done.

Keywords

Bond market Gaussian processes Nonsemimartingales Short rates Volatility Cox–Ingersoll–Ross model 

Notes

Acknowledgements

The work of José Manuel Corcuera and Gergely Farkas is supported by the MCI Grant No. MTM2009-08218.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • José Manuel Corcuera
    • 1
    Email author
  • Gergely Farkas
    • 2
  • Wim Schoutens
    • 3
  • Esko Valkeila
    • 4
  1. 1.Universitat de BarcelonaBarcelonaSpain
  2. 2.Universitat de BarcelonaBarcelonaSpain
  3. 3.K.U. LeuvenLeuvenBelgium
  4. 4.Department of Mathematics and Systems AnalysisAalto UniversityAaltoFinland

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