Portfolio Risk Measurement via Stochastic Mesh with Average Weight

Nested simulation has been widely used in the risk measurement of derivative portfolio. The convergence rate of the mean squared error (MSE) of the standard nested simulation is $k^{-2/3}$ , where $k$ is the simulation budget. To speed the convergence, we propose a stochastic mesh approach with average weight to portfolio risk measurement under the nested setting. We establish the asymptotic properties of the stochastic mesh estimator for portfolio risk, including the bias, variance and then the MSE. In particular, we show that the MSE converges to zero at a rate of $k^{-1}$ , which is the same as that under the non-nested setting. The proposed method also allows for path dependence of financial instruments in the portfolio. Numerical experiments show that the proposed method performs well.