市场风险的高效率加速算法研究

在计算投资组合市场风险时,采用高效率重要性抽样技术来处理大规模、高维度和稀有事件问题可以提高计算的速度和效率。在对投资组合损失进行Delta-Gamma近似的基础上,通过利用辅助分布变换函数,将求解抽样参数的最小抽样方差问题转化为一个非线性的广义最小二乘问题;在指数族抽样核的假设下,进一步将问题转化为迭代线性回归问题,从而简化了计算;通过德尔塔对冲和指数对冲投资组合的模拟算例验证了所提出方法的有效性。

Efficient Importance Sampling for Value at Risk

In order to dealf with large scale,high dimension and rare event problem,we apply the efficient importance sampling method for computing Value-at-Risk of a portfolio.Firstly,building on Delta-Gamma approximations to changes in portfolio value and by replacing the initial sampler by an auxiliary parametric importance sampler,the optimal choices for the sampling parameters are given by solving a nonlinear Generalized Least Squares problem.Secondly,under the assumption of density kernels within the exponential family of distributions,the problem is further simplified to solving a linear regression problem.Finally,Numerical examples of Delta and Index hedged portfolios demonstrate the good performance of the proposed methods.