Abstract
We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. Combining this new estimator with multilevel Monte Carlo (MLMC) leads to an estimator with a computational complexity that is similar to the complexity of a MLMC estimator when applied to options with Lipschitz payoffs.
| Original language | English |
|---|---|
| Pages (from-to) | 4836-4862 |
| Number of pages | 27 |
| Journal | Annals of Applied Probability |
| Volume | 34 |
| Issue number | 5 |
| Early online date | 26 Sept 2024 |
| DOIs | |
| Publication status | Published - Oct 2024 |
Keywords
- Monte Carlo
- branching processes
- computational complexity
- multilevel
- path splitting
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty