Risk Estimation via Regression
作者提出了一种基于回归的嵌套蒙特卡洛模拟方法，用于估计金融风险。外层模拟生成风险因子，内层模拟根据风险因子结果对证券定价并计算投资组合损失。标准嵌套模拟的均方误差以计算量k的-2/3次方速率收敛。新方法通过结合不同风险因子实现的信息，更准确地估计投资组合损失函数，其均方误差以k的-1次方速率收敛，直到达到取决于回归误差大小的渐近偏差水平。数值结果与理论分析一致，并与其他方法进行了比较。
We introduce a regression-based nested Monte Carlo simulation method for the estimation of financial risk. An outer simulation level is used to generate financial risk factors and an inner simulation level is used to price securities and compute portfolio losses given risk factor outcomes. The mean squared error (MSE) of standard nested simulation converges at the rate k −2/3 , where k measures computational effort. The proposed regression method combines information from different risk factor realizations to provide a better estimate of the portfolio loss function. The MSE of the regression method converges at the rate k −1 until reaching an asymptotic bias level which depends on the magnitude of the regression error. Numerical results consistent with our theoretical analysis are provided and numerical comparisons with other methods are also given.