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

Bull, Adam D.

Ann. Stat. 44, No. 1, 58-86 (2016).

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.

Reviewer: Marius Iosifescu (Bucureşti)

MSC:

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)

Keywords:

Blumenthal-Getoor index; Lévy process; infinite variation; jump activity; semimartingale

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