组合风险的重要性抽样方法

Importance Sampling Method for Portfolio Risk

摘要:

针对资产组合的市场风险或信用风险的任意边际分布的Gaussian Copula模型，首先将损失转化成高维正态分布的函数，然后对该模型进行重要性采样蒙特卡罗模拟以提高模拟效率，并分别使用牛顿法和基于大偏差理论估计测度变换的系数，并在此基础上提出了常数凝固估计法.数值实验表明，提出的算法与通常的蒙特卡罗方法相比，大大减小了模拟误差，从而提高了计算效率.

Abstract:

Based on the Gaussian Copula model with arbitrary marginal distribution in portfolio’s market risk or credit risk; To improve the efficiency in Monte Carlo simulation with importance sampling, we first transform loss to a function of a high dimensional normal vector, then the Newton’s method and a method based on the large deviation theory are used to estimate the coefficients in measure transformation, and the method of freezing coefficient is also proposed. Numerical experiments show that compared with standard Monte Carlo method, the algorithm proposed in the paper reduce simulation error greatly and therefore improve computational efficiency.