Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: application to financial returns

TL;DR

This paper develops a two-tailed Hawkes model to analyze asymmetric self- and cross-excitation of extreme gains and losses in financial returns, revealing that losses have a stronger and quicker impact than gains.

Contribution

It introduces a novel two-tailed Hawkes model capturing asymmetries in extreme events and applies it to financial data to uncover differential excitation effects.

Findings

Losses contribute twice as much as gains to the intensity.

The decay of loss excitation is nearly five times faster than that of gains.

Market reactions to losses are more immediate and intense.

Abstract

We construct a two-tailed peak-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.