The computation of important risk measures such as Value-at-Risk (VaR) or expected shortfall (ESF) contributions using Monte Carlo (MC) simulation becomes a challenging task when heavy-tailed loss distributions are involved. In Operational Risk (OR) one is usually confronted with such types of distributions and thus forced to use a large number of scenarios to obtain numerically stable estimates of aggregate risk capital (i.e. VaR). However, the computation of ESF tail contributions required for the allocation of capital at divisional level is even more difficult to stabilize, which makes straightforward MC simulation often impracticable for this purpose.

Asmussen and Kroese have successfully employed a variance-reducing methodology for the rare event simulation with heavy tails: conditional Monte Carlo estimators.

This presentation describes the general technique of conditional MC simulations as well as its application within the LDA. Furthermore, the implementation in DB's AMA model for the calculation of contributory capital for the different cells of our business line/event type matrix via expected shortfall contributions is introduced. The perfomance of the Asmussen-Kroese algorithm and plain MC are compared to demonstrate the superiority of conditional MC.