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Parisian time of reflected Brownian motion with drift on rays and its application in banking

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  • Dassios, Angelos
  • Zhang, Junyi

Abstract

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper was motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit. We reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results to the existing literature.

Suggested Citation

  • Dassios, Angelos & Zhang, Junyi, 2020. "Parisian time of reflected Brownian motion with drift on rays and its application in banking," LSE Research Online Documents on Economics 107495, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:107495
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    File URL: http://eprints.lse.ac.uk/107495/
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    References listed on IDEAS

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    1. Soramäki, Kimmo & Bech, Morten L. & Arnold, Jeffrey & Glass, Robert J. & Beyeler, Walter E., 2007. "The topology of interbank payment flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 317-333.
    2. Jean-Charles Rochet & Jean Tirole, 1996. "Controlling risk in payment systems," Proceedings, Board of Governors of the Federal Reserve System (U.S.), pages 832-869.
    3. Morten Linnemann Bech & Umar Faruqui & Takeshi Shirakami, 2020. "Payments without borders," BIS Quarterly Review, Bank for International Settlements, March.
    4. Christopher Becher & Marco Galbiati & Merxe Tudela, 2008. "The timing and funding of CHAPS sterling payments," Economic Policy Review, Federal Reserve Bank of New York, vol. 14(Sep), pages 113-133.
    5. J. Anderluh & J. Weide, 2009. "Double-sided Parisian option pricing," Finance and Stochastics, Springer, vol. 13(2), pages 205-238, April.
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    More about this item

    Keywords

    Brownian motion; Parisian time; exact simulation; real-time gross settlement system;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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