Volatility and jump activity estimation in a stable Cox-Ingersoll-Ross model

2024/07/31 by Elise Bayraktar, Bayraktar, Elise, Emmanuelle Clément +1 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2407.21411

openalex created_date 2024/07/26 · openalex publication_date 2024/07/31 · openalex updated_date 2026/07/28

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 (2020), 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.

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• Efficient estimation of jump parameters for stochastic differential equations driven by Lévy processes

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