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 language | English |
|---|---|
| Pages (from-to) | 189-204 |
| Number of pages | 16 |
| Journal | Methodology and Computing in Applied Probability |
| Volume | 20 |
| Issue number | 1 |
| Early online date | 25 Jan 2017 |
| DOIs | |
| Publication status | Published - 1 Mar 2018 |
Keywords
- Drawdown stopping time
- Monte Carlo simulation
- Multiple drawdown options
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Dassios, A., & Lim, J. W. (2018). An Efficient Algorithm for Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion. Methodology and Computing in Applied Probability, 20(1), 189-204. https://doi.org/10.1007/s11009-017-9542-y