Observations on industry practice in the construction of large correlation structures for risk and capital margins
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This is a practical paper, concerned with certain existing industry practices used to factor large correlation matrices into estimates of variance of total portfolio liabilities, and hence into risk, and possibly capital margins, and the extent to which those practices are theoretically sound. Two such practices are examined, and the results of this enquiry are largely negative. One practice appears to be fatally flawed. It is found to produce an estimated variance of total liabilities from the variance of subsets of the total that is not consistent with any particular correlation matrix between those subsets other than in trivial circumstances. The other approach lacks the support of any formulated stochastic model of the liabilities. While such a model may exist (as yet unformulated), the author has not succeeded in identifying it. The “most obvious” contender has been tested, and found wanting.
KeywordsCapital margin Correlation matrix Industry practice Loss reserving Risk margin Tensor product
I wish to acknowledge the valuable assistance of Phuong Anh Vu in discussing and commenting on the draft of this paper, particularly in relation to the proofs of lemmas and theorems.
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