Near-optimal estimation of jump activity in semimartingales. (English) Zbl 1334.62179

Author’s abstract: 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.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62M02 Markov processes: hypothesis testing
62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
62F25 Parametric tolerance and confidence regions
60G48 Generalizations of martingales
60G51 Processes with independent increments; Lévy processes
60J75 Jump processes (MSC2010)
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