An Efficient Algorithm for Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion

Angelos Dassios, Jia Wei Lim*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

4 Citations (Scopus)
227 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)189-204
Number of pages16
JournalMethodology and Computing in Applied Probability
Volume20
Issue number1
Early online date25 Jan 2017
DOIs
Publication statusPublished - 1 Mar 2018

Keywords

  • Drawdown stopping time
  • Monte Carlo simulation
  • Multiple drawdown options

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