Modeling Financial Contagion Using Mutually Exciting Jump Processes

Abstract

Sydney, the AFMATH Conference in Brussels, the Cambridge-Princeton Conference and the TCF Workshop on Lessons from the Credit Crisis, and in particular to Kenneth Lindsay, for their comments and suggestions. This research was funded in part by the NSF under grant SES-0850533 (Aït-Sahalia) and by the NWO under grants Veni-2006 and Vidi-2009 (Laeven). Matlab code to implement the estimation procedure developed in this paper is available from the authors upon request. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

“…Our results are in accord with them but we go further and allow two different channels through diffusion volatility and the jump intensity. This also differentiates us from existing papers where either only the diffusion channel is present (Eraker, Johannes, and Polson, 2003;Eraker, 2004) or only the jump intensity is affected by return jumps (Aït-Sahalia, Cacho-Diaz, and Laeven, 2010;Carr and Wu, 2010). We find that the diffusion channel is more important and remains significant even when the jump channel is allowed.…”

“…Consequently, another extreme movement in asset price is highly likely to be followed, even if there is no jump arrival. Another strand proposes a mechanism whereby jumps in asset returns feedback to the jump intensity, leading to self-excitation (Aït-Sahalia, Cacho-Diaz, and Laeven, 2010;Carr and Wu, 2010). Here, large jumps in asset returns increase the likelihood of extreme events in future asset returns and generate aggregate volatility jumps through the jump intensity.…”

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

“…The classical econometric literature, such as [9,32,33,34,35], employ the Hawkes model with the exponential kernel ϕ(t) = α exp(−βt), which is not normalized and require the estimation of the two parameters {α, β}, which just have to obey the conditions α, β > 0. In contrast, the explicit definition of the branching ratio n = α/β (see Eq.…”

“…The monovariate Hawkes process with, for instance, exponential kernel (5) and constant background activity is fully described with a set of only 3 parameters (µ, n and τ ). With the addition of one dimension and accounting for the cross-excitation (bi-variate model that is used, for instance, in [9,47,34,35,48]), the parameter set is increased to 10 parameters when no symmetry is imposed. The six-variate Hawkes model suggested in [10] is parametrized by 78 parameters in the general case.…”

Partial information about contagion risk, self-exciting processes and portfolio optimization

“…We show that exactly this specification induces self-exciting loss intensities. Recent empirical evidence by Ait-Sahalia, Cacho-Diaz, and Laeven (2012) suggests that this model class fits stock dynamics very well. Intuitively, our model captures events such as the 'Black Thursday ', October 24, 1929.…”