信用风险组合尾部概率估计的重要抽样算法优化

发布时间：2018-02-09 10:18

  本文关键词： 信用风险组合 罕见事件 尾概率 经典两步重要抽样算法 零方差原则 最大值原则 重要分布函数 中心极限定理 Metroplis—Hastings算法　出处：《南京大学》2017年硕士论文　论文类型：学位论文

【摘要】：信用风险组合发生大额损失是一件罕见事件,但是一旦发生将造成严重后果。为了有效管理罕见事件发生造成的影响,首要任务是估计出罕见事件发生的概率,或尾概率。在计算中,由于罕见事件发生的概率很小,样本量很少,从而导致估计方差过大。目前经典的两步重要抽样算法在解决此问题时取得一定的成果,但是经典方法在构造风险因子重要分布函数时采用零方差原则和最大值原则,得到的重要分布函数与理想状况相差较大。本文根据零方差原则结合中心极限定理构造了新的重要分布函数,并通过Metropolis-Hastings算法抽取风险因子的样本,最终有效地减小了尾概率估计的方差。数据分析方面,通过与一般蒙特卡罗方法和经典的两步重要抽样方法作数值比较,发现本文提出的算法能够明显减小尾概率估计的方差,得到预期效果。
[Abstract]:The occurrence of large portfolio credit risk loss is a rare event, but the event will cause serious consequences. In order to have the impact of effective management of the rare event, the first task is to estimate the probability of rare events, or tail probability. In the calculation, the probability of rare events is very small, small amount of sample, which leads to the estimation variance is too large. The classic two step important sampling algorithm made some achievements in solving this problem, but the classical method in constructing the important risk factor distribution function with zero variance principle and maximum principle, important distribution function and ideal conditions are different. According to the principle of combining the zero variance central limit theorem the distribution function of the new structure, and the risk factor of the sample Metropolis-Hastings algorithm, finally effectively reduces the variance of tail probability estimation. In the aspect of data analysis, by comparing with general Monte Carlo method and classic two step importance sampling method, it is found that the algorithm proposed in this paper can significantly reduce the variance of tail probability estimation and get the expected effect.

【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.2
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本文编号：1497702