ASYMPTOTIC EXPANSIONS FOR HIGH-FREQUENCY OPTION DATA

• 成果类型: Article
• 署名作者: Chong, Carsten H.; Todorov, Viktor
• 署名单位: Hong Kong University of Science & Technology; Northwestern University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2163
• 发表日期: 2025
• 页码: 1941-1979
• 关键词: INTEGRATED VOLATILITY; spot volatility; leverage; distributions; prices; models

摘要

We derive a nonparametric higher-order asymptotic expansion for smalltime changes of conditional characteristic functions of It & ocirc; semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of the increment of the underlying process and the time gap between evaluating the conditional characteristic function are shrinking. The spot semimartingale characteristics of the underlying process as well as their spot semimartingale characteristics appear as leading terms in the derived asymptotic expansions. The analysis applies to a general class of It & ocirc; semimartingales that includes in particular L & eacute;vy-driven SDEs and time-changed L & eacute;vy processes. The asymptotic expansion results are subsequently used to construct a test for whether volatility jumps are of finite or infinite variation. In an application to high-frequency data of options written on the S&P 500 index, we find evidence for infinite variation volatility jumps.