PERFECT HEDGING IN ROUGH HESTON MODELS

• 成果类型: Article
• 署名作者: El Euch, Omar; Rosenbaum, Mathieu
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1408
• 发表日期: 2018
• 页码: 3813-3856
• 关键词: stochastic volatility; hawkes processes

摘要

Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian motion. We show in this paper that surprisingly enough, explicit hedging strategies can be obtained in the case of rough Heston models. The replicating portfolios contain the underlying asset and the forward variance curve, and lead to perfect hedging (at least theoretically). From a probabilistic point of view, our study enables us to disentangle the infinite-dimensional Markovian structure associated to rough volatility models.