Bias Correction Estimation for Continuous-Time Asset Return Model with Jumps

TL;DR

This paper develops local linear estimators for continuous-time asset return models with jumps, effectively correcting bias and demonstrating their consistency and normality, with practical application to high-frequency stock data.

Contribution

It introduces a bias correction method using local linear estimators for jump-diffusion models, applicable to both finite and infinite activity jumps, with proven theoretical properties.

Findings

Estimators are weakly consistent and asymptotically normal.

Simulation shows effective bias correction in various jump scenarios.

Empirical application to high-frequency stock returns demonstrates practical utility.

Abstract

In this paper, local linear estimators are adapted for the unknown infinitesimal coefficients associated with continuous-time asset return model with jumps, which can correct the bias automatically due to their simple bias representation. The integrated diffusion models with jumps, especially infinite activity jumps are mainly investigated. In addition, under mild conditions, the weak consistency and asymptotic normality is provided through the conditional Lindeberg theorem. Furthermore, our method presents advantages in bias correction through simulation whether jumps belong to the finite activity case or infinite activity case. Finally, the estimators are illustrated empirically through the returns for stock index under five-minute high sampling frequency for real application.