By Greg N. Gregoriou (eds.)

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4 Finally, a rule of thumb to decide the number of bins is that k ≥ 3 and Ej ≥ 5 for all j. Severity distribution The severity distribution models the economic impact of operational risk loss events. Consequently, any strictly positive continuous distribution can be used to model operational losses. However, operational risk databases are often characterized by a large bulk of “high frequency/low impact” losses and a few “low frequency/high impact” losses. Leptokurtic distributions are thus most appropriate to model the severity distribution.

J. and Palm, F. (2001) “Tail-Index Estimates in Small Samples”, Journal of Business and Economic Statistics, 19(1): 208–16. H. E. (1998) Loss Models – From Data to Decisions (New York: Wiley Series on Probability and Statistics). N. (1933) “Sulla Determinazione Empiricadi una Legge di Distribuzione”, Giornale dell’ Istituto Attuari, 4: 83–91. M. D. (2000) Simulation Modeling and Analysis, 3rd edn (New York: McGraw-Hill). Longin, F. and Solnik, B. (2001) “Extreme Correlation of International Equity Markets”, Journal of Finance, 56(2): 649–76.

As illustrated in the remainder of this example, beyond serving as an effective means to hedge risk and ensure portfolio acceptability, the derivative reduces the amount of riskfree capital required to be held by the firm. 8) Consider the portfolio η = [1, 1, 0] consisting of one unit of riskfree capital, one unit of the first risky asset and none of the second. The portfolio η is not acceptable since the payoff is negative if the coin toss results in tails. In the coherent risk measure framework, η requires an additional unit of riskfree capital resulting in η∗ADEH = [2, 1, 0] .

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