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Risk aggregation and Extreme Events [37]

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Bullet points include: Portfolio with n loans to different obligors and i’th obligor defaults over a given time period if a latent variable zi falls below a cut-off -ci Exposures assumed to be ‘binary’, i.e. either defaulted or not (but can generalise to multiple non-default rating categories) If zi Normally distributed and N(.) is cumulative Normal distribution then probability of default of i’th obligor is: Suppose zi satisfy factor structure, where x and i are independent unit Normals:

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