This post presents a recent paper by Gkillas, Longin and Tsagkanos (2017). This paper introduces a new model with asymmetric time-exceedance of extreme shocks defined with optimal threshold derived from extreme value theory. It has implications in economics and finance.

Concept

We propose an innovative model, entitled asymmetric exceedance time model with optimal threshold, by combing the extreme value theory (distribution tails models) with regression techniques. Building on works related to the asymmetric phenomenon which has been widely documented in economic, finance and statistics, we examine the concept of asymmetry in extreme volatile periods. We use extreme value theory (peak-over-threshold method) to model extremes. We propose a procedure for the automatic computation of optimal thresholds, at the point where the fitting of the extreme value distribution is maximized. We define extreme shocks as exceedances over the optimal threshold and determine how the duration between past and present extreme shocks affects the dependent variable, introducing the temporal variability of extreme events.

Application

We present an empirical application to the exchange and equity markets. The mechanism of interactions between these markets is substantial for many outstanding issues in international economics and finance. Furthermore, both in theoretical and empirical literature, there is not consensus between the economic relation which connect these markets. We use daily data from S&P 500 and GBP/USD.

In this application we explore whether investors’ memory of past extreme events has a feedback effect at the time of an extreme shock. In other words, we separate the investors’ direct perceptions from the investors’ indirect expectations based on their memory. Our empirical findings suggest that the investors’ reaction at the time of an extreme shock is significantly affected by their memory and are consistent with the ‘portfolio balance’ models.

Usefulness

The understanding of interactions among financial variables in extreme volatile periods is crucial for several reasons. For example, theoretical economic models can be tested in extreme conditions or empirical findings can be useful in practice for asset managers (building portfolios based on diversification) and risk managers (defining hedging strategies against adverse events). However, the model is general and can be applied in any time series with heavy tails.

Reference: Gkillas K., F. Longin and A. Tsagkanos (2017) “Asymmetric Exceedance-Time Model: An Optimal Threshold Approach Based on Extreme Value Theory”. Available at SSRN: https://ssrn.com/abstract=3016145

Konstantinos Gkillas
University of Patras