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A note on transition density for the reflected Ornstein–Uhlenbeck process

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  • Xing, Xiaoyu
  • Xing, Yongsheng
  • Yang, Xuewei

Abstract

This note focuses on the Ornstein–Uhlenbeck process reflected at its long-run level (or long-run mean). The analytical closed-form of the transition density is obtained by virtue of the Skorokhod equation and the time-change for martingales. Our result is consistent with that presented by Linetsky (2005). Finally, an open problem concerning the general cases (reflected at an arbitrary level) is proposed.

Suggested Citation

  • Xing, Xiaoyu & Xing, Yongsheng & Yang, Xuewei, 2012. "A note on transition density for the reflected Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 586-591.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:586-591
    DOI: 10.1016/j.spl.2011.11.019
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    References listed on IDEAS

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    1. Lijun Bo & Dan Tang & Yongjin Wang & Xuewei Yang, 2011. "On the conditional default probability in a regulated market: a structural approach," Quantitative Finance, Taylor & Francis Journals, vol. 11(12), pages 1695-1702.
    2. Chuang Yi, 2010. "On the first passage time distribution of an Ornstein-Uhlenbeck process," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 957-960.
    3. Olivier Scaillet & Boris Leblanc, 1998. "Path dependent options on yields in the affine term structure model," Finance and Stochastics, Springer, vol. 2(4), pages 349-367.
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    Cited by:

    1. Archil Gulisashvili, 2020. "Large deviation principles for stochastic volatility models with reflection and three faces of the Stein and Stein model," Papers 2006.15431, arXiv.org.

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