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Extreme value theory

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Value at risk

The Journal of Operational Risk

Operational losses are true dangers for banks, since their maximal values to signal default are difficult to predict. In this paper, we analyze data from a very large US bank and show that it could suffer, on average, more than four major losses a year. The bank had seven losses exceeding hundreds of millions of dollars among its 52 documented losses of more than US$1 million over the 1994-2004 period. The tail of the loss distribution predicts that this bank is in danger of experiencing extreme operational losses ranging from $1 billion (with 1% probability) to $11 billion (0.1% probability). The corresponding annual insurance premiums are estimated to range from $350 million to almost $1 billion.

A practical application of extreme value theory to operational risk in banks