WEAK ERROR ESTIMATES FOR ROUGH VOLATILITY MODELS

• 成果类型: Article
• 署名作者: Friz, Peter k.; Salkeld, William; Wagenhofer, Thomas
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Nottingham; Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2109
• 发表日期: 2025
• 页码: 64-98
• 关键词: numerical schemes; driven; rates

摘要

We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for such (non-Markovian) models concerns efficient numerical schemes. While strong rates are well understood (order H), we tackle here the intricate question of weak rates. Our main result asserts that the weak rate, for a reasonably large class of test function, is essentially of order min13H + 12, 1} where HE (0, 1/2] is the Hurst parameter of the fractional Brownian motion that underlies the rough volatility process. Interestingly, the phase transition at H = 1/6 is related to the correlation between the two driving factors, and thus gives additional meaning to a quantity already of central importance in stochastic volatility modelling. Our results are complemented by a lower bound which show that the obtained weak rate is indeed optimal.