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Multivariate Hawkes processes: an application to financial data

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Paul Embrechts ,
Thomas Liniger  and
Lu Lin
Paul Embrechts
Affiliation:
ETH Zürich and Swiss Finance Institute, RiskLab, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Email address: embrechts@math.ethz.ch
Thomas Liniger
Affiliation:
ETH Zürich, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Lu Lin
Affiliation:
ETH Zürich, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
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Abstract

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A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

Keywords

Multivariate Hawkes processpoint processclusteringself-exciting

MSC classification

Primary: 60G55: Point processes

Information

Type
Part 8. Point Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 367 - 378
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Aït-Sahalia, Y., Cacho-Diaz, J. and Laeven, R. J. A., (2011). Modeling financial contagion using mutually exciting jump processes. To appear in Rev. Financial Studies.Google Scholar
[2] Azizpour, S., Giesecke, K. and Schwenkler, G., (2010). Exploring the sources of default clustering. Preprint. Stanford University.Google Scholar
[3] Brémaud, P., (1981). Point Processes and Queues. Springer, New York.CrossRefGoogle Scholar
[4] Brémaud, P. and Massoulié, L., (1996). Stability of nonlinear Hawkes processes. Ann. Prob. 24, 1563–1588.CrossRefGoogle Scholar
[5] Chavez-Demoulin, V., Davison, A. C. and McNeil, A. J., (2005). Estimating value-at-risk: a point process approach. Quant. Finance 5, 227–234.CrossRefGoogle Scholar
[6] Daley, D. J. and Vere-Jones, D., (2003). An Introduction to the Theory of Point Processes. Vol. I, 2nd edn. Springer, New York.Google Scholar
[7] Embrechts, P., Klüppelberg, C. and Mikosch, T., (1997). Modelling Extremal Events. Springer, Berlin.Google Scholar
[8] Errais, E., Giesecke, K. and Goldberg, L. R., (2010). Affine point processes and portfolio credit risk. SIAM J. Financial Math. 1, 642–665.Google Scholar
[9] Hawkes, A. G., (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 83–90.Google Scholar
[10] Lin, L., (2010). An Application of Multivariate Hawkes Process to Finance. , Department of Mathematics, ETH Zürich.Google Scholar
[11] Liniger, T., (2009). Multivariate Hawkes Processes. , Department of Mathematics, ETH Zürich.Google Scholar
[12] McNeil, A. J., Frey, R. and Embrechts, P., (2005). Quantitative Risk Management. Princeton University Press, Princeton, NJ.Google Scholar
[13] Meyer, P. A., (1971). Démonstration simplifiée d'un théorème de Knight. In Séminaire de Probabilités, V (Lecture Notes Math. 191), Springer, Berlin, pp. 191–195.Google Scholar
[14] Oakes, D., (1975). The Markovian self-exciting process. J. Appl. Prob. 12, 69–77.Google Scholar
[15] Ogata, Y., (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83, 9–27.Google Scholar
[16] Ogata, Y., (1998). Space-time point-process models for earthquake occurrences. Ann. Inst. Statist. Math. 50, 379–402.Google Scholar
[17] Papangelou, F., (1972). Integrability of expected increments of point processes and a related change of scale. Trans. Amer. Math. Soc. 165, 483–506.CrossRefGoogle Scholar
[18] Watanabe, S., (1964). On discontinuous additive functionals and Lévy measures of a Markov process. Japanese J. Math. 34, 53–70.Google Scholar