Modeling Risk via Realized HYGARCH Model

TL;DR

This paper introduces the realized Hyperbolic GARCH model, a flexible approach for modeling financial returns that captures long memory and leverage effects, and demonstrates its effectiveness in risk forecasting through simulation studies.

Contribution

It generalizes existing realized GARCH models by incorporating hyperbolic dynamics and studies its stationarity and forecasting performance.

Findings

RHYGARCH-GG outperforms in VaR and ES forecasting

Gaussian-Gaussian errors yield better risk estimates

Model captures long memory and leverage effects effectively

Abstract

In this paper, we propose the realized Hyperbolic GARCH model for the joint-dynamics of lowfrequency returns and realized measures that generalizes the realized GARCH model of Hansen et al.(2012) as well as the FLoGARCH model introduced by Vander Elst (2015). This model is sufficiently flexible to capture both long memory and asymmetries related to leverage effects. In addition, we will study the strictly and weak stationarity conditions of the model. To evaluate its performance, experimental simulations, using the Monte Carlo method, are made to forecast the Value at Risk (VaR) and the Expected Shortfall (ES). These simulation studies show that for ES and VaR forecasting, the realized Hyperbolic GARCH (RHYGARCH-GG) model with Gaussian-Gaussian errors provide more adequate estimates than the realized Hyperbolic GARCH model with student- Gaussian errors.