英文标题：
《Efficient Exponential Tilting for Portfolio Credit Risk》
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作者：
Cheng-Der Fuh, Chuan-Ju Wang
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最新提交年份：
2019
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英文摘要：
  This paper considers the problem of measuring the credit risk in portfolios of loans, bonds, and other instruments subject to possible default under multi-factor models. Due to the amount of the portfolio, the heterogeneous effect of obligors, and the phenomena that default events are rare and mutually dependent, it is difficult to calculate portfolio credit risk either by means of direct analysis or crude Monte Carlo under such models. To capture the extreme dependence among obligors, we provide an efficient simulation method for multi-factor models with a normal mixture copula that allows the multivariate defaults to have an asymmetric distribution, while most of the literature focuses on simulating one-dimensional cases. To this end, we first propose a general account of an importance sampling algorithm based on an unconventional exponential embedding, which is related to the classical sufficient statistic. Note that this innovative tilting device is more suitable for the multivariate normal mixture model than traditional one-parameter tilting methods and is of independent interest. Next, by utilizing a fast computational method for how the rare event occurs and the proposed importance sampling method, we provide an efficient simulation algorithm to estimate the probability that the portfolio incurs large losses under the normal mixture copula. Here the proposed simulation device is based on importance sampling for a joint probability other than the conditional probability used in previous studies. Theoretical investigations and simulation studies, which include an empirical example, are given to illustrate the method.
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中文摘要：
本文研究了在多因素模型下，贷款、债券和其他可能违约的工具组合的信用风险度量问题。由于投资组合的数量、债务人的异质效应以及违约事件罕见且相互依赖的现象，在此类模型下，很难通过直接分析或粗略的蒙特卡罗方法计算投资组合信用风险。为了捕捉债务人之间的极端依赖性，我们为具有正态混合copula的多因素模型提供了一种有效的模拟方法，该方法允许多变量违约具有非对称分布，而大多数文献侧重于模拟一维情况。为此，我们首先提出了一种基于非常规指数嵌入的重要性抽样算法，该算法与经典的充分统计量有关。注意，与传统的单参数倾斜方法相比，这种创新的倾斜装置更适合多元正态混合模型，并且具有独立的意义。接下来，通过利用罕见事件如何发生的快速计算方法和提出的重要性抽样方法，我们提供了一种有效的模拟算法，以估计在正态混合copula下投资组合发生重大损失的概率。在此，所提出的模拟装置基于联合概率的重要性抽样，而不是先前研究中使用的条件概率。通过理论研究和仿真研究，包括一个实例，对该方法进行了说明。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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