Modeling financial contagion using mutually exciting jump processes

Abstract

JEL classification: C58 G01 G15 C32Keywords: Jumps Contagion Crisis Hawkes process Self-and mutually exciting processes a b s t r a c t We propose a model to capture the dynamics of asset returns, with periods of crises that are characterized by contagion. In the model, a jump in one region of the world increases the intensity of jumps both in the same region (self-excitation) as well as in other regions (cross-excitation), generating episodes of highly clustered jumps across world markets that mimic the observed features of the data. We develop and implement moment-based estimation and testing procedures for this model. The estimates provide evidence of selfexcitation both in the US and the other world markets, and of asymmetric crossexcitation, with the US market typically having more influence on the jump intensity of other markets than the reverse. We propose filtered values of the jump intensities as a measure of market stress and examine their out-of-sample forecasting abilities.

Estimation of the Continuous and Discontinuous Leverage Effects

“…This is consistent with the finding that 5-seconds returns are positively correlated, which might be explained by self- and/or mutual excitation in jumps (see e.g. Aït-Sahalia et al (2015) and Boswijk et al (2015)). For instance, it could be the case that occurred jumps tend to excite other jumps with the same sign in the short run.…”

Multivariate dynamic intensity peaks‐over‐threshold models

“…The proposed class of processes generates a flexible and computationally tractable multivariate dependence structure—properties that in recent years have been empirically well documented in other contexts by Bowsher (), Bacry, Dayri, and Muzy (), Bacry, Delattre, Hoffmann, and Muzy (), Aït‐Sahalia, Laeven, and Pelizzon (), and Aït‐Sahalia et al. (), among others. Accordingly, our framework allows us to analyze how the effect of the occurrence of an extreme event is traced through the system and dynamically affects the other processes.…”

“…Traditional concepts to describe the tail of a loss distribution are value‐at‐risk (VaR) and expected shortfall (ES); see, for example, McNeil and Frey (), Cotter and Dowd (), or Chavez‐Demoulin, Embrechts, and Sardy (). On the other hand, point process methods allow the dynamic behavior of (extreme) events to be captured and are typically applied in the context of portfolio credit risk, market microstructure analysis, contagion analysis, or jump‐diffusion models; see, for example, Engle and Russell (), Bauwens and Hautsch (), Errais, Giesecke, and Goldberg (), Bacry and Muzy (), or Aït‐Sahalia, Cacho‐Diaz, and Laeven (). Moreover, point process theory provides an elegant formulation for the characterization of the limiting distribution of extreme value distributions, see Pickands () or Smith (), and therefore builds a natural complementary framework to extreme value analysis.…”

Dyadic event attribution in social networks with mixtures of hawkes processes

“…One important self-exciting process is the Hawkes process, which was first used to analyze earthquakes [13], and later applied to a wide range of tasks such as market modeling [5, 2], crime modeling [16], terrorist [14], conflict [18], and viral videos on the Web [4]. An EM framework was proposed to estimate the maximum likelihood of Hawkes processes [11].…”