基于双层嵌套模拟的条件期望方差估计与VaR计算

THE ESTIMATOR OF THE VARIANCE OF CONDITIONAL EXPECTATION AND THE CALCULATION OF VALUE AT RISK BASED ON THE TWO-LEVEL NESTED SIMULATION

在双层嵌套模拟中,通常外层模拟生成场景,内层样本估计在给定场景下的条件期望方差.所引入场景效应和观察误差随机变量,使条件期望的方差估计量是无偏的,并且讨论了计算量一定的情况下使估计量的方差达到最小的最优内层样本容量.然后,将该方法运用到金融风险度量中,分析了收益率均值和标准差对VaR的影响.最后,基于双层嵌套模拟提出一种估计VaR的新方法,该方法既能有效地处理非线性非正态的情形,又在一定程度上解决了参数选择的问题.实证研究结果通过了频率失败检验,说明该方法的合理有效性.

In a two-level nested simulation, the outer level of simulation usually generates different scenarios, and the inner level is used to estimate conditional ex-pectation of a given scenario. In this paper, first we obtain the unbiased estimator of the variance of the conditional expectation by introducing two random variables - the effect of a scenario and the observing error. In a fixed computational budget, to minimize the estimator＇s variance, we discuss the optimal number of inner-level samples. Then we apply this method to financiM risk measure. We also analyze the influence of different parameters on VaR. Finally, we propose a new method of calcu- lating VaR. This new method is able to deal well with nonlinear non-normal situation, and can also solve the problem of choosing parameters in a sense. The result obtained by the new method succeeds in the Kupiec efficency of this method. test, which illustrates the rationality and efficency of this method.