违约回收率密度函数模拟的非参数估计方法研究

发布时间：2018-02-01 07:49

本文关键词： 违约回收率非参数估计核函数最优窗宽边界问题　出处：《系统工程理论与实践》2014年S1期 　论文类型：期刊论文

【摘要】：本文研究违约回收率密度函数的模拟估计问题.本文的工作由两个方面组成.首先,我们解决了在应用非参数方法估计违约回收率密度函数时如何选取窗宽,以及在使用对称核时如何处理在有界区间上产生的边界问题.针对如何选取合理窗宽提高估计效果的问题,我们通过将最优窗宽选取通过渐近积分误差最小作为标准,然后将满足渐近积分误差最小的问题转换为一个非线性方程,进而应用插入法与迭代算法,求出最优窗宽的收敛解.第二,针对应用普通对称核拟合分布于[0,1]区间内的回收率会产生的估计量偏差在边界有增大趋势问题,我们通过引入边界核来改善这一现象:首先对两种核的统计性质进行理论推导,随后使用蒙特卡罗模拟(Monte Carlo Simulation)方法对其拟合绩效进行数值分析.本文的数值结果表明我们引入边界核方法,这较之普通对称核可以有效改善边界问题,同时边界核方法在各个指标上效果更优.最后,基于穆迪公司官方网站公布的2006年到2011年全球每年违约公司债券和贷款的违约回收率统计数据共653个数据,我们的实证案例分析表明,本文引入的边界核方法与现有普遍使用的以Beta分布刻画回收率的方法相比较,通过拟合优度检验和Bootstrap检验,我们的违约回收率密度函数模拟的非参数边界核方法比对应的Beta分布刻画方法更可靠,同时我们的结果也明显优于Beta分布刻画的回收率模型.
[Abstract]:This paper studies the simulation estimation of default recovery rate density function. The work of this paper is composed of two aspects. Firstly, we solve the problem of how to select window width when using nonparametric method to estimate default recovery density function. And how to deal with the boundary problem in the bounded interval when using symmetric kernel, aiming at how to select the reasonable window width to improve the estimation effect. By selecting the minimum error of the asymptotic integration of the optimal window width as the criterion, the problem satisfying the minimum of the asymptotic integral error is transformed into a nonlinear equation, and then the interpolation method and the iterative algorithm are applied. The convergence solution of the optimal window width is obtained. Secondly, the general symmetric kernel is used to fit the distribution. [In the range of 0 ~ 1, the deviation of the estimated quantity will increase at the boundary. We improve this phenomenon by introducing the boundary kernels: firstly, the statistical properties of the two kinds of kernels are theoretically deduced. Then Monte Carlo simulation Monte Carlo simulation method is used to analyze its performance. The numerical results show that we introduce the boundary kernel method. This method can effectively improve the boundary problem compared with the ordinary symmetric kernel, and the boundary kernel method is more effective in each index. Finally. Based on the statistics of default recovery rate of defaulted corporate bonds and loans published by Moody's website from 2006 to 2011, our empirical case study shows that 653 data are available. The boundary kernel method introduced in this paper is compared with the commonly used Beta distribution to describe the recovery rate. The goodness of fit test and Bootstrap test are adopted. Our nonparametric boundary kernel method is more reliable than the corresponding Beta distribution method, and our results are obviously superior to the Beta distribution model.
【作者单位】：浙江财经大学金融学院;浙江财经大学财富管理与量化投资协同创新中心;浙江省政府管制与公共政策研究中心;同济大学风险管理研究所;
【基金】：国家自然科学基金(71171176) 同济大学千人计划和引进人才计划基金(139206)
【分类号】：F832.51;F224;F203
【正文快照】： i引言信用风险一直是金融行业风险管理的最为核心的问题,比如,2010年9月出炉的业界极为关注的《巴塞尔协议III〉〉中对影响金融资产信用风险的三大主要因素是:1)违约概率(PD);2)违约损失率(LGD)(其中,回收率(RR)=1-违约损失率;即两者之和为1,因而可以相互转化)和3)违约风险暴

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