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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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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.

Keywords

Drawdown stopping time Monte Carlo simulation Multiple drawdown options 

Mathematics Subject Classification (2010)

65C05 65C50 
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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of StatisticsLondon School of EconomicsLondonUK
  2. 2.School of MathematicsUniversity of BristolBristolUK

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