Asymmetries and interactions between two tails of extreme returns in financial price time series

Abstract

The long-term trajectory of complex systems is often dominated by rare, outsized events that cluster together in time. This has spurred the development of conditional extreme value theory (EVT), where the arrivals and magnitudes of these extreme events are modelled independently from the bulk of the distribution. Price changes, as measured by log returns, are an atypical case study because they feature opposing left and right tails of extremes (i.e. losses and gains) that are highly correlated yet asymmetric. This presents an intriguing potential for complex asymmetric interactions between the two tails. If identified, these may yield signals that enhance the forecasting of future extremes and provide new insight into the collective behaviour of traders that generates price changes.

To probe this, we construct a novel two-tailed peaks-over-threshold (2T-POT) Hawkes model that captures asymmetric self- and cross-excitation between the left- and right-tail extremes within a time series. In a large-scale study, we apply our model to the daily log returns of six large-cap equity indices; we take the unique step of repeating this over a wide range of exceedance thresholds, from the 1.25% to 25.00% mirrored in-sample quantiles. We observe that the arrivals of extreme losses and gains are described by a common intensity and that this intensity is significantly more excited by losses compared to gains, which is consistent with conventional descriptions of the leverage effect in conditional volatility models (GJR-GARCH). But, in a novel insight, our model also finds that the excitement from losses decays much more quickly.

To test the predictive power of this temporal leverage effect, we adapt the 2T-POT Hawkes model to produce forecasts of conditional quantile-based tail risk measures. In our large-scale study, out-of-sample convergence tests find that our approach provides more accurate and reliable forecasting of one-step-ahead extreme left- and right-tail conditional quantiles compared to the benchmark GJR-GARCH-EVT model. Having thus demonstrated its significance, we seek to identify a lower level generating mechanism for the temporal leverage effect by proposing a general structural stochastic volatility agent-based model (GSSV-ABM) in which we add a novel volatility targeting strategy to the classic trend–value dyad of chartists and fundamentalists.

Date of Award	2 Oct 2024
Original language	English
Awarding Institution	University of Bath
Supervisor	Marcin Mucha-Kruczynski (Supervisor), David Greenwood (Supervisor) & Andreas Krause (Supervisor)