Parametric estimation of hidden stochastic model by contrast minimization and deconvolution: application to the Stochastic Volatility Model

TL;DR

This paper introduces a new parametric estimation method for hidden stochastic models like the Stochastic Volatility model, using contrast minimization and deconvolution, which is faster and more robust than classical methods.

Contribution

The paper proposes a novel contrast minimization and deconvolution approach for estimating hidden stochastic models, demonstrating improved speed and robustness over traditional methods.

Findings

Outperforms Maximum Likelihood in computation time

More robust to non-Gaussian errors

Does not require tuning parameters

Abstract

We study a new parametric approach for particular hidden stochastic models such as the Stochastic Volatility model. This method is based on contrast minimization and deconvolution. After proving consistency and asymptotic normality of the estimation leading to asymptotic confidence intervals, we provide a thorough numerical study, which compares most of the classical methods that are used in practice (Quasi Maximum Likelihood estimator, Simulated Expectation Maximization Likelihood estimator and Bayesian estimators). We prove that our estimator clearly outperforms the Maximum Likelihood Estimator in term of computing time, but also most of the other methods. We also show that this contrast method is the most robust with respect to non Gaussianity of the error and also does not need any tuning parameter.