Analysis of High Frequency Financial Data: Models, Methods and Software. Part II: Modeling and Forecasting Realized Variance Measures

A key problem in financial econometrics is the modeling, estimation and forecasting of conditional return volatility and correlation. Having accurate forecasting models for conditional volatility and correlation is important for accurate derivatives pricing, risk management and asset allocation decisions. It is well known that conditional volatility and correlation are highly predictable. An inherent problem with modeling and forecasting conditional volatility is that it is unobservable, which implies that modeling must be indirect. Popular parametric models for latent volatility include the ARCH-GARCH family, the stochastic volatility family, and the Markov-switching family. In these models volatility is usually extracted from daily squared returns, which are unbiased but noisy estimates of daily conditional volatility. High frequency data is rarely utilized. The estimation of these models, however, often give unsatisfactory results. In particular, forecasts are imprecise. Moreover, standardized returns generally have fat-tails which has led to the search for appropriate error distributions that can adequately capture empirical return distributions. Furthermore, multivariate modeling of volatility and correlation can be extremely difficult and practical models are often only feasible for very low dimensions. An exciting new area of research involves estimating, modeling and forecasting conditional volatility and correlation using high frequency intra-day data. The justification for using high frequency data follows from recent research that shows that daily conditional volatility and correlation can be accurately estimated using so-called realized volatility and correlation measures, which are based on summing high frequency squared returns and cross products of returns. Now, instead of using complicated models for unobserved volatility one can use more straightforward models for observed volatility. This use of high frequency data has the potential of revolutionizing the way volatility and correlation are modeled and forecasted.