MULTILEVEL PATH BRANCHING FOR DIGITAL OPTIONS

• 成果类型: Article
• 署名作者: Giles, Michael b.; Aji-ali, Abdul-lateef
• 署名单位: University of Oxford; Heriot Watt University; University of Edinburgh
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2083
• 发表日期: 2024
• 页码: 4836-4862
• 关键词: monte-carlo; integration

摘要

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.