An asymmetric ARCH model and the non-stationarity of Clustering and Leverage effects

TL;DR

This paper introduces a new asymmetric ARCH volatility model capturing clustering and leverage effects, analyzing their time evolution and non-stationarity using extensive Dow Jones data.

Contribution

The paper presents a novel asymmetric ARCH model that explains short-term leverage effects and long-term clustering, with empirical calibration over 77 years of Dow Jones data.

Findings

Short-term volatility is influenced by the sign of past returns.

Long-term volatility is dominated by clustering effects.

Clustering and leverage effects show complex non-stationary behavior over time.

Abstract

We propose a new volatility model based on two stylized facts of the volatility in the stock market: clustering and leverage effect. We calibrate our model parameters, in the leading order, with 77 years Dow Jones Industrial Average data. We find in the short time scale (10 to 50 days) the future volatility is sensitive to the sign of past returns, i.e. asymmetric feedback or leverage effect. However, in the long time scale (300 to 1000 days) clustering becomes the main factor. We study non-stationary features by using moving windows and find that clustering and leverage effects display time evolutions that are rather nontrivial. The structure of our model allows us to shed light on a few surprising facts recently found by Chicheportiche and Bouchaud.