Spectral estimation of the L\'evy density in partially observed affine models

TL;DR

This paper introduces a new spectral estimation method for the Le9vy density in partially observed affine models, achieving optimal convergence rates and demonstrating effectiveness in the Bates stochastic volatility model.

Contribution

It develops a novel spectral estimation approach for Le9vy densities in affine processes using log-affine characteristic functions and local linear smoothing, with proven optimal convergence rates.

Findings

Achieves almost sure uniform convergence rates for Le9vy density estimates.

Demonstrates optimality of convergence rates in a minimax sense.

Validates the method with simulations in the Bates stochastic volatility model.

Abstract

The problem of estimating the L\'evy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the conditional characteristic function of an affine process and local linear smoothing in time. We derive almost sure uniform rates of convergence for the estimated L\'evy density both in mixed-frequency and low-frequency setups and prove that these rates are optimal in the minimax sense. Finally, the performance of the estimation algorithms is illustrated in the case of the Bates stochastic volatility model.