Michel Dacorogna, Tail-Dependence an Essential Factor for

More documents

Recommendations

Info

AcknowledgementThis work is based on a team effort by:Roland Bürgi who programmed the whole analysis anddeveloped a method to generate hierarchical multivariatedistributions with copulasRoger IlesAnd Michel DacorognaTail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 20123Agenda1 Risk-Adjusted Capital and dependence2 Description of the model3 Influence of the number of observations on calibration4 Influence of dependence structure and models5 Ways to model the dependence6 ConclusionTail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 20124
Determining Risk-Adjusted CapitalThe Risk-Adjusted capital (RAC) of an insurance company isevaluated on the basis of a quantitative model of its differentrisksWe first need to identify the various sources of risk. Oneusually distinguishes four large risk categories:1. Underwriting risk (or liability risk),2. Investment risk (or asset risk),3. Credit risk (or risk of default),4. Operational riskGenerally insurance companies have the know-how tomanage and model their liability risk and are able to modelthe next two categories as well using standard finance modelsTail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 20125Dependence Between Risks is KeyRisk Diversification reduces a company’s need for Risk-Adjusted capital. This is key to both insurance and investments.However, risks are rarely completely independent:• Stock market crashes are usually not limited to one stock market.• Certain lines of business are affected by economic cycles, likeaviation, credit & surety or life insurances.• Motor insurance is also correlated to motor liability insurance andboth will vary during economic cycles.• Big catastrophes can produce claims in various lines of business.Dependence between risks reduces the benefits ofdiversification.The influence of dependence on the aggregated RAC is thuscrucial and needs to be carefully analyzed.Tail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 20126
Page 1: Tail-Dependence an Essential Factor
Page 5 and 6: Agenda1 Risk-Adjusted Capital and d
Page 7 and 8: The Lognormal DistributionLognormal
Page 9 and 10: Elliptical Copula: Rank Correlation
Page 13 and 14: Estimation of CopulasThe following
Page 15 and 16: Convergence of the Fits for 4 Margi
Page 17 and 18: Results of Fit: Clayton FlatAs expe
Page 19 and 20: Results of Fit: Rank Correlation Fl
Page 21 and 22: Dependence Model mattersmore than D
Page 23 and 24: Strategy for modeling dependencesUs

Michel Dacorogna, Tail-Dependence an Essential Factor for

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?