Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo
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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 strong consistent. 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)+ϵ) for arbitrarily small ϵ>0. The numerical results show that the RQMC method performs better than the Monte Carlo method for all cases. The gain of plain RQMC declines as the dimension d increases, as predicted by the established theoretical error rate.
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