PORTFOLIO RISK MEASUREMENT VIA STOCHASTIC MESH

We propose a stochastic mesh approach to portfolio risk measurement under the nested setting in which revaluation of the portfolio value requires simulations. While stochastic mesh was originally proposed as a tool for American option pricing, we are interested in estimating via simulation the risk of the portfolio. We establish asymptotic properties of the stochastic mesh estimator for portfolio risk. In particular, we show that the estimator is asymptotically unbiased and consistent, and its mean squared error (MSE) converges to zero in a rate of Γ⁻¹ , where Γ is the effort required to simulate the sample paths. This rate of convergence is the same as that under the non-nested setting. The proposed method allows for path dependence of financial instruments in the portfolio. Preliminary numerical experiments show that the proposed method works reasonably well.