Mutual Excitation in Eurozone Sovereign CDS

TLDR: In this paper, the authors study self-excitation and crossexcitation of shocks in the Eurozone sovereign CDS market and derive closed-form formulae for CDS prices, and estimate the model by matching theoretical prices to their empirical counterparts.

Abstract: We study self- and cross-excitation of shocks in the Eurozone sovereign CDS market. We adopt a multivariate setting with credit default intensities driven by mutually exciting jump processes, to capture the salient features observed in the data, in particular, the clustering of high default probabilities both in time (over days) and in space (across countries). The feedback between jump events and the intensity of these jumps is the key element of the model. We derive closed-form formulae for CDS prices, and estimate the model by matching theoretical prices to their empirical counterparts. We find evidence of self-excitation and asymmetric cross-excitation. Using impulse-response analysis, we assess the impact of shocks and a potential policy intervention not just on a single country under scrutiny but also, through the effect on cross-excitation risk which generates systemic sovereign risk, on other interconnected countries.

Figures

Fig. 1. S&P sovereign ratings for Greece, Portugal and Spain.

Fig. 5. Sovereign CDS; and Impulse-Response Analysis in a Network Graph.

Fig. 4. CDS Italy, Spain and Portugal; and CDS Portugal and Italy.

Table 1. Summary Statistics CDS Spreads. This table reports summary statistics for daily changes (measured in bps) of sovereign CDS spreads for France (FR), Germany (DE), Greece (GR), Ireland (IE), Italy (IT), Portugal (PT) and Spain (ES). The mean levels of the spreads themselves are also reported (in bps). Sample period IE, IT, ES, 5-year CDS FR: January 1, 2007, to August 31, 2012. Sample period GR: January 1, 2007, to March 8, 2012. Sample period PT: December 17, 2007 to August 31, 2012. Sample period DE and 10-year FR: December 21, 2007, to August 31, 2012.

Fig. 9. Simulated Sample Paths.

Fig. 8. Impulse-Response Analysis along the Time Dimension: Shock in Ireland.

Full text

Aït-Sahalia, Yacine; Laeven, Roger J. A.; Pelizzon, Loriana
Working Paper
Mutual excitation in eurozone sovereign CDS
SAFE Working Paper, No. 51
Provided in Cooperation with:
Leibniz Institute for Financial Research SAFE
Suggested Citation: Aït-Sahalia, Yacine; Laeven, Roger J. A.; Pelizzon, Loriana (2014) :
Mutual excitation in eurozone sovereign CDS, SAFE Working Paper, No. 51, Goethe University
Frankfurt, SAFE - Sustainable Architecture for Finance in Europe, Frankfurt a. M.,
https://doi.org/10.2139/ssrn.2438625
This Version is available at:
http://hdl.handle.net/10419/97496
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Yacine Aït-Sahalia - Roger J. A. Laeven - Loriana Pelizzon
Mutual Excitation in Eurozone Sovereign
CDS
Working Paper Series No. 51

Non-Technical Summary
Past crises as well as the recent global financial crisis and the Eurozone sovereign debt crisis
have highlighted the fact that extreme events, such as jumps in asset prices, as well as the
events that are relevant for the assessment of the default probability of a given debt
instrument, including credit rating changes, tend to occur not in isolation but in clusters, both
in time as well as across debt issuers, whether those issuers are countries (sovereigns) or firms
(corporates).
Credit default swaps (CDS) are derivative instruments which provide insurance against the risk
of default by a debt issuer. As such, their spreads provide key information about the cost of
such insurance and, consequently, the market's view about the arrival rate of default events.
Therefore, they are ideal instruments to investigate default probability itself and cross-
excitation both in time and across debt issuers.
This paper proposes and investigates a model designed around a specific feedback mechanism
to capture the dependencies among the risk of the different Eurozone countries. The feedback
element introduces a propagation dimension from one shock to the next and one sovereign to
the next that is not present in common factor models. Motivated by the current Eurozone
sovereign debt crisis, we study whether CDS contracts that insure sovereign European debt are
priced consistently with the predictions of the model, including the clustering that is apparent
in the underlying credit-relevant events.
The analysis of the data reveals i) that Eurozone CDS rates, and hence default intensities,
exhibit clusters in time and in space; ii) transmission of shocks that is rapid but not
instantaneous; and iii) asymmetry in the extent to which a shock in one sovereign affects the
others.
The broad empirical implications of the model are reassuring for its plausibility and realism:
Ireland, Portugal, Spain and Italy are the main countries affected by events in Greece, with
results varying in strength across the countries, and to a lesser extent France and Germany.
This finding and the analysis surrounding it has important practical implications. Using the
estimated model, we perform an impulse-response analysis, a commonly used tool in
macroeconometrics, by shocking the system and examining how shocks affecting CDS prices
transmit throughout the Eurozone.
We use the results to assess the impact of a capital injection not just on a single country, but
also its potential reduction of the spillover to other countries. By inferring the patterns of
excitation flowing from one country to another, we can identify the countries where a policy
intervention would be most effective, at least with the objective of lowering CDS rates across
the board in the Eurozone. Because CDS rates are important inputs to many financial decisions,
and they are heavily watched by market participants, it is not unreasonable to view lowering

them as an objective in itself towards restoring confidence in the stability of the Eurozone. In
particular, the asymmetry in the way contagion flows means that there is potential for
intervention in one CDS market to be more successful than in others. We find for example that
a policy intervention in Ireland resulting in an exogenous lowering of the CDS rate there would
have been much less effective than a similar policy intervention in Greece.

Mutual Excitation in Eurozone Sovereign CDS
Yacine A¨ıt-Sahalia
†
Department of Economics
Bendheim Center for Finance
Princeton Uni versity
and NBER
Roger J. A. Laeven
‡
Dept. of Quantitative Economics
Amsterdam School of Econ omi cs
University of Amsterdam
EURANDOM and CentER
Loriana Pelizzon
§
Department of Economics
Ca’ Foscari University of Venice
and SAFE-Goethe Unive r s ity
Frankfurt
This Version: May 14, 2014
Abstract
We study self- and cross-excitation of shocks in the Eurozone sovereign CDS market. We adopt
a multivariate setting with credit default intensities driven by mutually exciting jump processes, to
capture the salient features observed in the dat a, in particular, the clustering of high default probabilities
both in time (over days) and in space (across countries). The feedback between jump events and the
intensity of these jumps is the key element of the model. We deri ve closed-form formulae for CDS
prices, and estimate the model by matching theoretical prices to their empirical counterparts. We find
evidence of self-excitation and asymmetric cross-e x ci t at ion . Using impulse-response analysis, we assess
the impact of shocks and a potential policy intervention not just on a single country under scrutiny
but also, through the e↵ect on cr oss -ex ci t at i on risk which generates systemic sove re i gn risk, on other
interconnected countries.
Key w ords and phrases: CDS; Sovereign risk; Systemic risk; J u mp s; Feedback; Hawkes processes; Mu-
tually exci t in g processes; Impulse-response.
JEL classification: C13; G12.
⇤
We are very grateful to the Editor, Alok Bhargava, and two anonymous referees for helpful comments and suggestions that
significantly improved the paper. We are also grateful to co n fere n ce participant s at the NBER Summer Institute Conference
2013 on Forecasting and Empirical Methods in Macro and Finance in Cambridge, Massachusetts, and the EFA Meeting
2013 in Cambridge, UK, for their comments and suggestion s. Finally, we acknowledge the excellent research assistance of
Lorenzo Frattarolo and the financial support in the form of a research grant fro m the Fondation Banque de France pour la
Recherche en Economie Mon´etaire, Financi`ere et Bancaire.This project has rece ived also funding from the European Un i on s
Seventh Framework Programme (FP7-SSH/2007-2013) for research, technological development and demon s t rat i o n under grant
agreement 320270 - SYRTO.
†
Princeton, NJ 08544-1021, USA. E-mail: yacine@princeton.edu. Research supported by the NSF under grant SES-0850533.
‡
1018 XE Amsterdam, The Netherlands. E-mail: R.J. A. La even@uva.nl. Research supported by the NWO under grant
Vidi-2009.
§
30121 Venezia, Italy. E-mail: loriana.pelizzon@unive.it. Research supported by the project SYRTO, European Union
under t h e 7th Framework Programme (FP7-SSH/2007-2013 - Grant Agreement n 320270), the project MISURA, funded by
the Italian MIUR and the SAFE Center, funded by the State of Hessen initiative for research LOEWE.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Mutual excitation in eurozone sovereign cds" ?

The authors study selfand cross-excitation of shocks in the Eurozone sovereign CDS market. Using impulse-response analysis, the authors assess the impact of shocks and a potential policy intervention not just on a single country under scrutiny but also, through the e↵ect on cross-excitation risk which generates systemic sovereign risk, on other interconnected countries.