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Real-World Forward Rate Dynamics With Affine Realizations

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Abstract

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.

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  • Eckhard Platen & Steffan Tappe, 2015. "Real-World Forward Rate Dynamics With Affine Realizations," Published Paper Series 2015-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:2015-7
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    File URL: https://www.tandfonline.com/doi/abs/10.1080/07362994.2015.1019629
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    Cited by:

    1. Toshiyuki Nakayama & Stefan Tappe, 2022. "Distance between closed sets and the solutions to stochastic partial differential equations," Papers 2205.00279, arXiv.org, revised Oct 2024.
    2. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    3. Tappe, Stefan, 2016. "Affine realizations with affine state processes for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2062-2091.
    4. Stefan Tappe, 2019. "Existence of affine realizations for stochastic partial differential equations driven by L\'evy processes," Papers 1907.00335, arXiv.org.
    5. Stefan Tappe, 2019. "Affine realizations with affine state processes for stochastic partial differential equations," Papers 1907.00336, arXiv.org.
    6. Claudio Fontana & Eckhard Platen & Stefan Tappe, 2024. "Real-world models for multiple term structures: a unifying HJM semimartingale framework," Papers 2411.01983, arXiv.org, revised Mar 2025.

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