Capturing Deep Tail Risk via Sequential Learning of Quantile Dynamics

Abstract

This paper develops a conditional quantile model that can learn long term and short term memories of sequential data. It builds on sequential neural networks and yet outputs interpretable dynamics. We apply the model to asset return time series across eleven asset classes using historical data from the 1960s to 2018. Our results reveal that it extracts not only the serial dependence structure in conditional volatility but also the memories buried deep in the tails of historical prices. We further evaluate its Value-at-Risk forecasts against a wide range of prevailing models. Our model outperforms the GARCH family as well as models using filtered historical simulation, conditional extreme value theory, and dynamic quantile regression. These studies indicate that conditional quantiles of asset return have persistent sources of risk that are not coming from those responsible for volatility clustering. These findings could have important implications for risk management in general and tail risk forecasts in particular.

Keywords: Dynamic Quantile Modeling, Parametric Quantile Functions, Time-varying Higher-order Conditional Moments, Asymmetric Heavy-tail Distribution, Long Short-term Memory, Machine Learning, Neural Network, VaR Forecasts, Financial Risk Management

JEL Classification: G32, C53, C45, C22