A dynamic contagion process for modelling contagion risk in finance and insurance
We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamics of contagion impact from endogenous and exogen...
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London School of Economics and Political Science (University of London)
2012
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ndltd-bl.uk-oai-ethos.bl.uk-5710582015-12-03T03:20:20ZA dynamic contagion process for modelling contagion risk in finance and insuranceZhao, Hongbiao2012We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamics of contagion impact from endogenous and exogenous factors of the underlying system. We systematically analyse the theoretical distributional properties of this new process, based on the piecewise-deterministic Markov process theory developed in Davis (1984), and the extension of the martingale methodology used in Dassios and Embrechts (1989). The analytic expressions of the Laplace transform of the intensity process and probability generating function of the point process are derived. A simulation algorithm is provided for further industrial implementation and statistical analysis. Some extensions of this process and comparison with other similar processes are also investigated. The major object of this study is to produce a general mathematical framework for modelling the dependence structure of arriving events with dynamic contagion, which has the potential to be applicable to a variety of problems in economics, finance and insurance. We apply our research to the default probability of credit risk and ruin probability of risk theory.330.01HA StatisticsLondon School of Economics and Political Science (University of London)http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.571058http://etheses.lse.ac.uk/489/Electronic Thesis or Dissertation |
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330.01 HA Statistics |
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330.01 HA Statistics Zhao, Hongbiao A dynamic contagion process for modelling contagion risk in finance and insurance |
description |
We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamics of contagion impact from endogenous and exogenous factors of the underlying system. We systematically analyse the theoretical distributional properties of this new process, based on the piecewise-deterministic Markov process theory developed in Davis (1984), and the extension of the martingale methodology used in Dassios and Embrechts (1989). The analytic expressions of the Laplace transform of the intensity process and probability generating function of the point process are derived. A simulation algorithm is provided for further industrial implementation and statistical analysis. Some extensions of this process and comparison with other similar processes are also investigated. The major object of this study is to produce a general mathematical framework for modelling the dependence structure of arriving events with dynamic contagion, which has the potential to be applicable to a variety of problems in economics, finance and insurance. We apply our research to the default probability of credit risk and ruin probability of risk theory. |
author |
Zhao, Hongbiao |
author_facet |
Zhao, Hongbiao |
author_sort |
Zhao, Hongbiao |
title |
A dynamic contagion process for modelling contagion risk in finance and insurance |
title_short |
A dynamic contagion process for modelling contagion risk in finance and insurance |
title_full |
A dynamic contagion process for modelling contagion risk in finance and insurance |
title_fullStr |
A dynamic contagion process for modelling contagion risk in finance and insurance |
title_full_unstemmed |
A dynamic contagion process for modelling contagion risk in finance and insurance |
title_sort |
dynamic contagion process for modelling contagion risk in finance and insurance |
publisher |
London School of Economics and Political Science (University of London) |
publishDate |
2012 |
url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.571058 |
work_keys_str_mv |
AT zhaohongbiao adynamiccontagionprocessformodellingcontagionriskinfinanceandinsurance AT zhaohongbiao dynamiccontagionprocessformodellingcontagionriskinfinanceandinsurance |
_version_ |
1718140783284977664 |