Bayesian Parametric Financial Risk Forecasting Employing Multiple High-Frequency Realized Measures

Abstract

This thesis aims to develop parametric volatility models that utilize multiple high-frequency realized volatility measures to forecast two types of tail risks: Value at Risk (VaR) and Expected Shortfall (ES). An extension of the realized exponential generalized autoregressive conditional heteroskedasticity model (realized EGARCH) is proposed, incorporating standardized Student t and skewed Student t distributions to model return equation errors. The realized EGARCH model employs robust realized volatility measures: subsampled realized variance (RVSS), subsampled realized range (RRSS), and realized kernel (RK). A Bayesian estimation technique outperforms maximum likelihood (ML) approach in simulation studies. The proposed models are empirically tested on seven market indices, demonstrating improved accuracy in tail risk prediction. Including RRSS, either individually or jointly with RVSS and/or RK, enhances the forecast performance of the model.

A variable selection method based on the Least Absolute Shrinkage and Selection Operator (Lasso) is proposed, employing cross-validation (CV) and Bayesian Lasso (BLasso) approaches. In the empirical study, RVSS, RRSS, RK, and Range variables are incorporated as realized volatility measures. Both CV and BLasso approaches indicate that RRSS and RVSS provide stronger signals about future volatility compared to RK and Range variables, with BLasso resulting in sparser realized EGARCH models.

Furthermore, an extension of the realized EGARCH model using a standardized two-sided Weibull distribution for return error distribution is proposed, with Bayesian estimation producing less biased and more precise parameter estimates than ML estimation. The empirical study demonstrates comparable forecast performance between the realized EGARCH models using standardized two-sided Weibull and standardized skewed Student t distributions, employing RVSS, RRSS, and RK.