Evidence on the Importance of Volatility Density Forecasting for Financial Risk Management

In this paper, we provide new empirical evidence of the relative usefulness of interval (density) and point forecasts of asset-return volatility, in the context of financial risk management using high frequency data. In our evaluation we use both statistical criteria (i.e., accuracy of directional volatility predictions) and economic criteria (i.e., profitability of trading strategies based on said predictions). We construct interval forecasts using nonparametric kernel estimators, while point forecasts are based on ``linear" heterogeneous autoregressive models as well as ``nonlinear" deep-learning recurrent neural network models. For our profitability analysis, we utilize a novel trading strategy that builds on the contemporaneous return-volatility relationship and leads to new insights related to linkages between economic and statistical methods of forecast evaluation. Our empirical findings indicate that interval forecasts can improve on point forecasts in terms of trading profitability (as measured using Sharpe and Sortino Ratios), regardless of the ``linear” or ``nonlinear" nature of the point-forecasting model. Moreover, linear (nonlinear) model-based point forecasts perform worse (marginally better) than interval forecasts when it comes to directional predictive accuracy. These findings are consistent with a number of hypotheses concerning both nonlinear volatility dynamics and the ability of interval forecasts to accurately estimate “large price jump” induced future volatility movements. A follow-up series of Monte Carlo experiments is motivated by our finding that for translation of statistical improvements into economic gains, the choice of volatility estimation technique is crucial. Our experiments reveal that the inability of certain nonparametric high frequency volatility estimators to accurately predict “pseudo true” volatility densities for specific magnitudes of “price jumps” and “microstructure noise” in the price process can explain why these same estimators are less profitable when used in our empirical trading strategies.