Volatility Forecasts Using Nonlinear Leverage Effects

TL;DR

This paper introduces a nonlinear leverage effect model within a Bayesian framework to improve volatility forecasts, demonstrating significant predictive improvements for most stocks in major indices.

Contribution

It proposes a flexible nonlinear leverage effect model and efficient Bayesian estimation to enhance volatility prediction accuracy.

Findings

Nonlinear leverage effects outperform linear models in 89% of stocks.

The model captures different impacts of small and large price fluctuations.

Improved density forecasts for a majority of tested stocks.

Abstract

The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts, empirical evidence paradoxically do not show that most individual stocks exhibit this phenomena, mischaracterizing risk and therefore leading to poor predictive performance. We examine this paradox, with the goal to improve density forecasts, by relaxing the assumption of linearity in the leverage effect. Nonlinear generalizations of the leverage effect are proposed within the Bayesian stochastic volatility framework in order to capture flexible leverage structures, where small fluctuations in prices have a different effect from large shocks. Efficient Bayesian sequential computation is developed and implemented to estimate this effect in a practical, on-line manner. Examining 615 stocks that comprise the S\&P500 and Nikkei 225, we find that relaxing the linear assumption to our proposed nonlinear leverage effect function improves predictive performances for 89\% of all stocks compared to the conventional model assumption.