  Computing risk measures of a financial portfolio comprising thousands of
derivatives is a challenging problem because (a) it involves a nested
expectation requiring multiple evaluations of the loss of the financial
portfolio for different risk scenarios and (b) evaluating the loss of the
portfolio is expensive and the cost increases with its size. In this work, we
look at applying Multilevel Monte Carlo (MLMC) with adaptive inner sampling to
this problem and discuss several practical considerations. In particular, we
discuss a sub-sampling strategy whose computational complexity does not
increase with the size of the portfolio. We also discuss several control
variates that significantly improve the efficiency of MLMC in our setting.
