Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T08:01:39.491Z Has data issue: false hasContentIssue false
  • English
  • Français

Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling

Published online by Cambridge University Press:  17 April 2015

Filip Lindskog  and
Alexander J. McNeil
Filip Lindskog
Affiliation:
Risklab, Federal Institute of Technology, ETH Zentrum, CH-8092 Zurich, Tel.: +41 1 632 67 41, Tel.: +41 1 632 10 85, [email protected]
Alexander J. McNeil
Affiliation:
Department of Mathematics, Federal Institute of Technology, ETH Zentrum, CH-8092 Zurich, Tel.: +41 1 632 61 62, Tel.: +41 1 632 15 23, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The idea of using common Poisson shock processes to model dependent event frequencies is well known in the reliability literature. In this paper we examine these models in the context of insurance loss modelling and credit risk modelling. To do this we set up a very general common shock framework for losses of a number of different types that allows for both dependence in loss frequencies across types and dependence in loss severities. Our aims are threefold: to demonstrate that the common shock model is a very natural way of approaching the modelling of dependent losses in an insurance or risk management context; to provide a summary of some analytical results concerning the nature of the dependence implied by the common shock specification; to examine the aggregate loss distribution that results from the model and its sensitivity to the specification of the model parameters.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 209 - 238
Copyright
Copyright © ASTIN Bulletin 2003

Footnotes

*

Research of the first author was supported by Credit Suisse Group, Swiss Re and UBS AG through RiskLab, Switzerland. We thank in particular Nicole Bäuerle for commenting on an earlier version of this paper.

References

Barlow, R., and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rine-hart & Winston, New York.Google Scholar
Credit-Suisse-Financial-Products (1997) CreditRisk+ a Credit Risk Management Framework. Technical Document, available from htpp://www.csfb.com/creditrisk.Google Scholar
Duffie, D., and Singleton, K. (1998) Simulating Correlated Defaults. Working paper, Graduate School of Business, Stanford University.Google Scholar
Embrechts, P., McNeil, A., and Straumann, D. (2001) Correlation and dependency in risk managements properties and pitfalls. In Risk Management: Value at Risk and Beyond, ed. by Dempster, M.. Cambridge university Press, Cambridge.Google Scholar
Frey, R., and Mcneil, A. (2001) Modelling dependent defaults. Preprint, ETH Zürich, available from http://www.math.ethz.ch/~frey.Google Scholar
Hogg, R., and Klugman, S. (1984) Loss Distributions. Wiley, New York.CrossRefGoogle Scholar
Jarrow, R., and Turnbull, S. (1995) Pricing Derivatives on Financial Securities Subject to Credit Risk. Journal of Finance, L(1), 83–85.Google Scholar
Joe, R. (1997) Multivariate Models and Dependence Concepts. Chapman & Hall, London.Google Scholar
KMV-Corporation (1997) Modelling Default Risk. Technical Document, available from http://www.kmv.com.Google Scholar
Li, D. (1999) On Default Correlation A Copula Function Approach. Working paper, RiskMetrics Group, New York.CrossRefGoogle Scholar
Li, H., and Xu, S. (2001) Stochastic bounds and dependence properties of survival times in a mul-ticomponent shock model. Journal of Multivariate Analysis 76, 63–89.CrossRefGoogle Scholar
Marshall, A., and Olkin, I. (1967) A multivariate exponential distribution. Journal of American Statistical Association 62, 30–44.CrossRefGoogle Scholar
Merton, R. (1974) On the Pricing of Corporate Debt The Risk Structure of Interest Rates. Journal of Finance 29, 449–470.Google Scholar
Nelsen, R.B. (1999) An Introduction to Copulas. Springer, New York.CrossRefGoogle Scholar
Panjer, H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
RiskMetrics-Group (1997) CreditMetrics – Technical Document, available from http://www.riskmetrics.com/research.Google Scholar
Rolski, T., Schmidli, H., Schmidt, V., and Teugels, J. (1998) Stochastic Processes for Insurance and Finance. Wiley, Chichester.Google Scholar
Savits, T. (1988) Some multivariate distributions derived from a non-fatal shock model. Journal of Applied Probability 25, 383–390.CrossRefGoogle Scholar
Schönbucher, P., and Schubert, D. (2001) Copula-dependent default risk in intensity models. Working paper.Google Scholar
Wang, S., and Dhaene, J. (1998) Comonotonicity, correlation order and premium principles. Insurance: Mathematics and Economics 22, 235–242.Google Scholar