A Bayesian Approach to Risk Management in a World of High-Frequency Data

Abstract

A Realised Volatility GARCH model using high-frequency data is developed within a Bayesian framework for the purpose of forecasting Value at Risk and Conditional Value at Risk. A Skewed Student-t return distribution is combined with a Student-t distribution in the measurement equation in a GARCH framework. Realised Volatility GARCH models show a marked improvement compared to ordinary GARCH. A Skewed Student-t Realised DCC copula model using Realised Volatility GARCH marginal functions is developed within a Bayesian framework for the purpose of forecasting portfolio tail risk. The use of copulas is implemented so that the marginal distributions can be separated from the dependence structure to produce tail forecasts. This is compared to using traditional GARCH-copula models, and GARCH on an aggregated portfolio. Copula models implementing a Realised Volatility GARCH framework show an improvement over traditional GARCH models. A Bayesian detection of regime changes utilizing high-frequency data is developed, once again for the purpose of forecasting portfolio tail risk. The use of high-frequency data improves the accuracy of regime change detection compared to daily data. Monte Carlo sampling schemes are employed for the estimation of these models.