Nonparametric Threshold Estimation for Drift Function in Jump–Diffusion Model of Interest Rate Using Asymmetric Kernel

The existing estimators for the drift coefficient in the diffusion model with jumps involve jump components and possess larger boundary error. How to effectively estimate the drift function is an important issue that faces challenges and has theoretical significance. In this paper, the gamma asymmet...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-05, Vol.11 (10), p.2281
Main Authors: Song, Yuping, Li, Chen, Wang, Hemin, Meng, Jiayi, Hao, Liang
Format: Article
Language:English
Subjects:
Analysis
Asymmetry
Asymptotic properties
bias reduction
Diffusion rate
drift coefficient
Drift estimation
Empirical analysis
Error correction
gamma asymmetrical kernel
Interest rates
jump–diffusion process
Kernels
Mathematical models
Mathematics
Money markets
Nonparametric statistics
Numerical analysis
Parameter estimation
Securities prices
short-term interest rate
Simulation methods
threshold function
Variables
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Summary:The existing estimators for the drift coefficient in the diffusion model with jumps involve jump components and possess larger boundary error. How to effectively estimate the drift function is an important issue that faces challenges and has theoretical significance. In this paper, the gamma asymmetric kernel for boundary correction and threshold function eliminating jump impacts are combined to estimate the unknown drift coefficient in the jump diffusion process of interest rate. The asymptotic large sample property and the better finite sample property through the Monte Carlo numerical simulation experiment and the empirical analysis of SHIBOR and LIBOR for the corresponding estimator are considered in detail. It is found that the estimator proposed in this paper can correct the estimation error near or far away from the origin point, which provides a more asymptotic unbiased estimator for the drift function in diffusion models with jumps.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11102281