Near-optimal estimation of jump activity in semimartingales

TL;DR

This paper introduces a new estimator for the jump activity index in semimartingales used in finance, achieving near-optimal convergence rates and demonstrating strong finite-sample performance.

Contribution

The paper presents a novel estimation method for jump activity that outperforms previous approaches in accuracy and convergence speed.

Findings

Achieves near-optimal rates of convergence.

Demonstrates strong finite-sample performance in simulations.

Provides confidence intervals for jump activity estimates.

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.