  Conditional value at risk (CVaR) is a popular measure for quantifying
portfolio risk. Sensitivity analysis of CVaR is very useful in risk management
and gradient-based optimization algorithms. In this paper, we study the
infinitesimal perturbation analysis estimator for CVaR sensitivity using
randomized quasi-Monte Carlo (RQMC) simulation. We first prove that the
RQMC-based estimator is strongly consistent under very mild conditions. Under
some technical conditions, RQMC that uses $d$-dimensional points in CVaR
sensitivity estimation yields a mean error rate of
$O(n^{-1/2-1/(4d-2)+\epsilon})$ for arbitrarily small $\epsilon>0$. The
numerical results show that the RQMC method performs better than the Monte
Carlo method for all cases. The gain of plain RQMC deteriorates as the
dimension $d$ increases, as predicted by the established theoretical error
rate.

Numerical Analysis;Numerical Analysis;Computation