M.A.R.C.: an Actuarial Model for Credit Risk - Proceedings ASTIN ...

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0 The provision of a further amount of money may be seen as a solvency margin for thebank. As said this quantity is usually equal to the difference between the valuecorresponding to a prefixed percentile (for example the 95th) and the expected loss;0 The losses exceeding the prefixed percentile may be considered catastrophic eventswhose probability is very low. This "catastrophic" loss might be continuously controlledby means of the proposed procedure.9. Conclusions and future lines of researchThe model presented in this paper is based on an actuarial approach: the single credit hasbeen considered as an insurance contract whose value depends on the occurrence of thedefault event.By taking into account the evolution of the default rates over the time we have described amethod to calculate the loss distribution of the entire portfolio.From the loss distribution some statistical indexes may be obtained and they are useful todecide upon adequate strategies of fimding and to quantify a solvency margin for the bank.In conclusion we think that the M.A.R.C. model seems a good tool for applying the typicaltechniques of the risk theory to credit portfolios. We deem that these techniques may pay animportant role in the active default risk management of banks and may create an importantlink between the actuarial science and the credit industrial sector.Bibliography1. Altman E.1- Saunders A. (1 998) Credit risk measurement: developments over the last 20years, Journal of banking and finance, (21198).2. Credit Suisse (1 997) CreditRisk+ A credit risk managementfiamework.3. Crouhy R. - Mark R. (1998) A comparative analysis of current credit risk models,Proceedings of the conference "Credit Modelling and the Regulatory Implications"(London 2 1 - 22 September 1998).4. Daykin C.D. - Pentikanen T. - Pesonen M. (1994) Practical risk theory for actuaries,Chapman & Hall.5. Hogg, R. V. - Klugman, S. A. (1984) Loss distributions, New York, Wiley.6. Koyluoglu H. U. - Hickman A. (1998) Reconciliable dzyerences, Risk (10198).7. McKynsey & Company (1 999) Creditporrfolio view - technical document;8. Micocci M. (1999) Un modello attuariale di valutazione e gestione del rischio creditizio,Proceedings of the XXIII AMASES.9. Panjer H. H. - Willmot G. E. (1 992) Insurance Risk Models Society of Actuaries.10. Szego G. - Varetto F. (1999) I1 rischio creditizio. Misura e controllo Utet;11. Wilson T. (1997) Porrfolio credit risk (I), Risk (9197).12. Wilson T. (1997) Porrfolio credit risk (II), Risk (10197).456
Appendix A1. The Weibull distributionProbability density hctionf(x)=a;O -n x a-l e -[;JDistribution~(x)= 1 - e -[STParametersa > 0,p > 02. The Lognormal distributionProbability density functionwhere-[lnx-wT1 -~~2u;DistributionNo closed formParametersp > 0,cr > 03. Beta distributionProbability density functionDistributionNo closed form457
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M.A.R.C.: an Actuarial Model for Credit Risk - Proceedings ASTIN ...

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