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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
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 120 (2010)
    Issue (Month): 2 (February)
    Pages: 163-181

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    Handle: RePEc:eee:spapps:v:120:y:2010:i:2:p:163-181

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    Related research

    Keywords: Affine processes Exponential martingale Uniform integrability Change of measure Exponential moments Generalized Riccati equation;

    References

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    1. Li Chen & Damir Filipović, 2005. "A simple model for credit migration and spread curves," Finance and Stochastics, Springer, vol. 9(2), pages 211-231, 04.
    2. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    3. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
    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.
    5. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    6. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382.
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    Cited by:
    1. Martin Keller-Ressel, 2014. "Simple examples of pure-jump strict local martingales," Papers 1405.2669, arXiv.org.
    2. 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.
    3. 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.

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