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

TL;DR

This paper develops rate-optimal estimators for volatility and jump activity in a stable Cox-Ingersoll-Ross model driven by Brownian motion and a stable Lévy process, addressing challenges from infinite variation jumps.

Contribution

It extends existing methods to jointly estimate volatility, scaling, and jump activity parameters in a stable CIR model with infinite variation jumps, achieving near rate-optimality.

Findings

Proposed estimators are rate optimal up to a logarithmic factor.

Extended approach from Mies (2020) to stable CIR models.

Addresses estimation challenges from infinite variation jumps.

Abstract

We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable L\'evy process with jump activity $\alpha \in (1,2)$. 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.