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An efficient algorithm for simulating the drawdown stopping time and the running maximum of a Brownian motion

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  • Dassios, Angelos
  • Lim, Jia Wei

Abstract

We define the drawdown stopping time of a Brownian motion as the first time its drawdown reaches a duration of length 1. In this paper, we propose an efficient algorithm to efficiently simulate the drawdown stopping time and the associated maximum at this time. The method is straightforward and fast to implement, and avoids simulating sample paths thus eliminating discretisation bias. We show how the simulation algorithm is useful for pricing more complicated derivatives such as multiple drawdown options.

Suggested Citation

  • Dassios, Angelos & Lim, Jia Wei, 2017. "An efficient algorithm for simulating the drawdown stopping time and the running maximum of a Brownian motion," LSE Research Online Documents on Economics 68823, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:68823
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    File URL: http://eprints.lse.ac.uk/68823/
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    Cited by:

    1. Angelos Dassios & Jia Wei Lim & Yan Qu, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1497-1526, October.

    More about this item

    Keywords

    Drawdown stopping time; Monte Carlo simulation; multiple drawdown options;
    All these keywords.

    JEL classification:

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

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