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Exponentially affine martingales, affine measure changes and exponential moments of affine processes

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  • Kallsen, Jan
  • Muhle-Karbe, Johannes

Abstract

We consider local martingales of exponential form or , where X denotes one component of a multivariate affine process. We give a weak sufficient criterion for M to be a true martingale. As a first application, we derive a simple sufficient condition for absolute continuity of the laws of two given affine processes. As a second application, we study whether the exponential moments of an affine process solve a generalized Riccati equation.

Suggested Citation

  • Kallsen, Jan & Muhle-Karbe, Johannes, 2010. "Exponentially affine martingales, affine measure changes and exponential moments of affine processes," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 163-181, February.
  • Handle: RePEc:eee:spapps:v:120:y:2010:i:2:p:163-181
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    References listed on IDEAS

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    4. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    6. Li Chen & Damir Filipović, 2005. "A simple model for credit migration and spread curves," Finance and Stochastics, Springer, vol. 9(2), pages 211-231, April.
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    Citations

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    Cited by:

    1. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    2. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Working Papers hal-01275397, HAL.
    3. repec:eee:dyncon:v:85:y:2017:i:c:p:59-89 is not listed on IDEAS
    4. repec:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0333-7 is not listed on IDEAS
    5. Keller-Ressel, Martin, 2015. "Simple examples of pure-jump strict local martingales," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4142-4153.
    6. Fred Espen Benth & Salvador Ortiz-Latorre, 2014. "A change of measure preserving the affine structure in the BNS model for commodity markets," Papers 1403.5236, arXiv.org.
    7. Martin Keller-Ressel, 2014. "Simple examples of pure-jump strict local martingales," Papers 1405.2669, arXiv.org, revised Jun 2015.
    8. Mayerhofer, Eberhard & Muhle-Karbe, Johannes & Smirnov, Alexander G., 2011. "A characterization of the martingale property of exponentially affine processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 568-582, March.
    9. Paolo Di Tella & Martin Haubold & Martin Keller-Ressel, 2017. "Semi-Static Variance-Optimal Hedging in Stochastic Volatility Models with Fourier Representation," Papers 1709.05527, arXiv.org.
    10. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Papers 1602.05541, arXiv.org, revised Feb 2016.
    11. Blanka Horvath & Antoine Jacquier & Peter Tankov, 2018. "Volatility options in rough volatility models," Papers 1802.01641, arXiv.org.

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