Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Realized Measures

TL;DR

This paper introduces a Bayesian semi-parametric Realized-CARE model that integrates realized measures into tail risk forecasting, demonstrating improved accuracy over traditional models in empirical financial data analysis.

Contribution

The paper develops a novel Realized-CARE framework with Bayesian estimation techniques, addressing convergence issues and enhancing tail risk forecasts using realized measures.

Findings

Outperforms traditional GARCH and CARE models in VaR and ES forecasting.

Incorporating Realized Range improves model accuracy.

Bayesian methods provide reliable parameter estimation.

Abstract

A new model framework called Realized Conditional Autoregressive Expectile (Realized-CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a manner analogous to the Realized-GARCH model. Competing realized measures (e.g. Realized Variance and Realized Range) are employed as the dependent variable in the measurement equation and to drive expectile dynamics. The measurement equation here models the contemporaneous dependence between the realized measure and the latent conditional expectile. We also propose employing the quantile loss function as the target criterion, instead of the conventional violation rate, during the expectile level grid search. For the proposed model, the usual search procedure and asymmetric least squares (ALS) optimization to estimate the expectile level and CARE parameters proves challenging and often fails to convergence. We incorporate a fast random walk Metropolis stochastic search method, combined with a more targeted grid search procedure, to allow reasonably fast and improved accuracy in estimation of this level and the associated model parameters. Given the convergence issue, Bayesian adaptive Markov Chain Monte Carlo methods are proposed for estimation, whilst their properties are assessed and compared with ALS via a simulation study. In a real forecasting study applied to 7 market indices and 2 individual asset returns, compared to the original CARE, the parametric GARCH and Realized-GARCH models, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed Realized-CARE model, especially when incorporating the Realized Range and the sub-sampled Realized Range as the realized measure in the model.