NEAR-OPTIMAL ESTIMATION OF JUMP ACTIVITY IN SEMIMARTINGALES

• 成果类型: Article
• 署名作者: Bull, Adam D.
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1349
• 发表日期: 2016
• 页码: 58-86
• 关键词: INTEGRATED VOLATILITY; activity index

摘要

In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimate of the jump activity, together with corresponding confidence intervals. Our estimate improves upon previous work, achieving near-optimal rates of convergence, and good finite-sample performance in Monte-Carlo experiments.