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Computing risk measures of a financial portfolio comprising thousands ofderivatives is a challenging problem because (a) it involves a nestedexpectation requiring multiple evaluations of the loss of the financialportfolio for different risk scenarios and (b) evaluating the loss of theportfolio is expensive and the cost increases with its size. In this work, welook at applying Multilevel Monte Carlo (MLMC) with adaptive inner sampling tothis problem and discuss several practical considerations. In particular, wediscuss a sub-sampling strategy whose computational complexity does notincrease with the size of the portfolio. We also discuss several controlvariates that significantly improve the efficiency of MLMC in our setting.

Sub-sampling and other considerations for efficient risk estimation in large portfolios