英文标题：
《Robust and Consistent Estimation of Generators in Credit Risk》
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作者：
Greig Smith and Goncalo dos Reis
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最新提交年份：
2017
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英文摘要：
Bond rating Transition Probability Matrices (TPMs) are built over a one-year time-frame and for many practical purposes, like the assessment of risk in portfolios or the computation of banking Capital Requirements (e.g. the new IFRS 9 regulation), one needs to compute the TPM and probabilities of default over a smaller time interval. In the context of continuous time Markov chains (CTMC) several deterministic and statistical algorithms have been proposed to estimate the generator matrix. We focus on the Expectation-Maximization (EM) algorithm by Bladt and Sorensen (2005) for a CTMC with an absorbing state for such estimation. This work\'s contribution is threefold. Firstly, we provide directly computable closed-form expressions for quantities appearing in the EM algorithm and associated information matrix, allowing to easily approximate confidence intervals. Previously, these quantities had to be estimated numerically and considerable computational speedups have been gained. Secondly, we prove convergence to a single set of parameters under very weak conditions (for the TPM problem). Finally, we provide a numerical benchmark of our results against other known algorithms, in particular, on several problems related to credit risk. The EM algorithm we propose, padded with the new formulas (and error criteria), outperforms other known algorithms in several metrics, in particular, with much less overestimation of probabilities of default in higher ratings than other statistical algorithms.
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中文摘要：
债券评级转移概率矩阵（TPM）是在一年的时间框架内建立的，出于许多实际目的，如评估投资组合中的风险或计算银行资本要求（如新的IFRS 9法规），需要在较小的时间间隔内计算TPM和违约概率。在连续时间马尔可夫链（CTMC）的背景下，提出了几种确定性和统计算法来估计生成器矩阵。我们关注Bladt和Sorensen（2005）针对具有吸收状态的CTMC的期望最大化（EM）算法。这项工作的贡献是三倍的。首先，我们为EM算法和相关信息矩阵中出现的数量提供了可直接计算的闭式表达式，从而可以方便地近似置信区间。以前，这些量必须用数字进行估计，并获得了相当大的计算速度。其次，我们证明了在非常弱的条件下（对于TPM问题）收敛到单个参数集。最后，我们提供了一个与其他已知算法相比的结果的数值基准，特别是在与信用风险相关的几个问题上。我们提出的EM算法，加上新的公式（和错误标准），在几个指标上优于其他已知算法，特别是在更高评级下，比其他统计算法高估的违约概率要少得多。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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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