Applied Mathematics & Optimization

, Volume 77, Issue 3, pp 405–441 | Cite as

Long-Term Yield in an Affine HJM Framework on \(S_{d}^{+}\)

  • Francesca Biagini
  • Alessandro Gnoatto
  • Maximilian Härtel


We develop the HJM framework for forward rates driven by affine processes on the state space of symmetric positive semidefinite matrices. In this setting we find an explicit representation for the long-term yield in terms of the model parameters. This generalises the results of El Karoui et al. (Rev Deriv Res 1(4):351–369, 1997) and Biagini and Härtel (Int J Theor Appl Financ 17(3):1–24, 2012), where the long-term yield is investigated under no-arbitrage assumptions in a HJM setting using Brownian motions and Lévy processes respectively.


HJM Affine process Long-term yield Yield curve Wishart process 



The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. [228087].


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Francesca Biagini
    • 1
    • 2
  • Alessandro Gnoatto
    • 1
  • Maximilian Härtel
    • 3
  1. 1.Department of MathematicsLMU UniversityMunichGermany
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.MEAG Munich ERGO AssetManagement GmbHMunichGermany

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