Self-Weighted Quantile Estimation for Drift Coefficients of Ornstein–Uhlenbeck Processes with Jumps and Its Application to Statistical Arbitrage

Yuping Song, Ruiqiu Chen, Chunchun Cai, Yuetong Zhang and Min Zhu ()
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Yuping Song: School of Finance and Business, Shanghai Normal University, Shanghai 200234, China
Ruiqiu Chen: Institute of Applied Economics, Shanghai Academy of Social Sciences, Shanghai 200020, China
Chunchun Cai: School of Finance and Business, Shanghai Normal University, Shanghai 200234, China
Yuetong Zhang: School of Mathematics, Shandong University, Jinan 250100, China
Min Zhu: School of Finance and Business, Shanghai Normal University, Shanghai 200234, China

Mathematics, 2025, vol. 13, issue 9, 1-31

Abstract: The estimation of drift parameters in the Ornstein–Uhlenbeck (O-U) process with jumps primarily employs methods such as maximum likelihood estimation, least squares estimation, and least absolute deviation estimation. These methods generally assume specific error distributions and finite variances. However, with the increasing uncertainty in financial markets, asset prices exhibit characteristics such as skewness and heavy tails, which lead to biases in traditional estimators. This paper proposes a self-weighted quantile estimator for the drift parameters of the O-U process with jumps and verifies its asymptotic normality under large samples, given certain assumptions. Furthermore, through Monte Carlo simulations, the proposed self-weighted quantile estimator is compared with least squares, quantile, and power variation estimators. The estimation performance is evaluated using metrics such as mean, standard deviation, and mean squared error (MSE). The simulation results show that the self-weighted quantile estimator proposed in this paper performs well across different metrics, such as 8.21% and 8.15% reduction of MSE at the 0.9 quantile for drift parameter γ and κ compared with the traditional quantile estimator. Finally, the proposed estimator is applied to inter-period statistical arbitrage of the CSI 300 Index Futures. The backtesting results indicate that the self-weighted quantile method proposed in this paper performs well in empirical applications.

Keywords: self-weighted quantile estimation; drift coefficients; O-U process with jumps; heavy-tailed distributions; statistical arbitrage; asymptotic normality; Monte Carlo simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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