Volatility prediction comparison via robust volatility proxies: An empirical deviation perspective

TL;DR

This paper compares volatility prediction methods using robust proxies, establishing deviation bounds and proposing a tuning-free Huber loss approach to improve forecast evaluation, especially with limited data.

Contribution

It introduces non-asymptotic deviation bounds for robust volatility proxies and a tuning-free Huber loss method for better volatility estimation in non-stationary markets.

Findings

Robust proxies provide more stable forecast evaluation with limited data.

The Huber approach adapts to non-stationary returns by jointly estimating volatility and robustification.

Empirical results on Bitcoin data demonstrate improved consistency in volatility forecast comparison.

Abstract

Volatility forecasting is crucial to risk management and portfolio construction. One particular challenge of assessing volatility forecasts is how to construct a robust proxy for the unknown true volatility. In this work, we show that the empirical loss comparison between two volatility predictors hinges on the deviation of the volatility proxy from the true volatility. We then establish non-asymptotic deviation bounds for three robust volatility proxies, two of which are based on clipped data, and the third of which is based on exponentially weighted Huber loss minimization. In particular, in order for the Huber approach to adapt to non-stationary financial returns, we propose to solve a tuning-free weighted Huber loss minimization problem to jointly estimate the volatility and the optimal robustification parameter at each time point. We then inflate this robustification parameter and use it to update the volatility proxy to achieve optimal balance between the bias and variance of the global empirical loss. We also extend this Huber method to construct volatility predictors. Finally, we exploit the proposed robust volatility proxy to compare different volatility predictors on the Bitcoin market data. It turns out that when the sample size is limited, applying the robust volatility proxy gives more consistent and stable evaluation of volatility forecasts.