Volatility and jump activity estimation in a stable Cox-Ingersoll-Ross model
Abstract
We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross (α-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable Lévy process with jump activity α∈(1,2). The main difficulties to obtain rate efficiency in estimating these quantities arise from the superposition of the diffusion component with jumps of infinite variation. Extending the approach proposed in Mies (Electron. J. Stat. 14 (2020) 4165–4206), we address the joint estimation of the volatility, scaling and jump activity parameters from high-frequency observations of the process and prove that the proposed estimators are rate optimal up to a logarithmic factor.
Fields of Study & Subjects
Stochastic processes and financial applications
Financial Risk and Volatility Modeling
Point processes and geometric inequalities
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 2
- Pages
- 926–951
- Publication date
- 29 January 2026
- Language
- EN