﻿ 基于KMV模型的上市公司债务违约概率度量与实证分析 Measurement and Empirical Analysis of Listed Companies Debt Default Probability via KMV Model

Statistics and Application
Vol. 08  No. 01 ( 2019 ), Article ID: 28351 , 12 pages
10.12677/SA.2019.81002

Measurement and Empirical Analysis of Listed Companies Debt Default Probability via KMV Model

Kaihao Liang*, A’yun Niu

College of Computational Science, Zhongkai University of Agriculture and Engineering, Guangzhou Guangdong

Received: Dec. 16th, 2018; accepted: Dec. 31st, 2018; published: Jan. 7th, 2019

ABSTRACT

How to measure the default risk of debt of listed companies has always been a hot topic in risk management. In this paper, KMV model is used to analyze relevant data of financial statements issued by listed companies in China, and the probability of their debt default is studied. The default probability of debt of listed companies based on KMV model is established, and the default probability of 41 listed companies in China’s securities market in 2012 is measured by the model. Meanwhile, 41 listed companies were divided into industries for similar analysis and inter-class analysis. The empirical results show that when the company’s asset-liability ratio is higher than 80%, regardless of its net asset liability ratio, it has a high credit risk, while when the company’s asset-liability ratio is lower than 50%, as long as there is no negative return on equity, the company is less likely to default.

Keywords:KVM Model, Default Probability, Listed Company, The Credit Risk

1. 研究背景和意义

2. KMV模型建立

KMV公司的KMV模型认为，当企业的资产低于全部债务价值的某个临界平时，企业一般会选择违约，并将这一临界点成为违约点(DPT)。它等于企业短期债务(STD)和一半长期债务(LTD)之和 [12] ：

$DPT=STD+\frac{\text{1}}{\text{2}}LTD$ (1)

$Q=prob\left[{V}_{t}\le DP{T}_{t}\right]$ (2)

$\frac{\text{d}{V}_{t}}{{V}_{t}}=\mu \text{d}t+\sigma \text{d}z$ (3)

${V}_{t}={V}_{0}\mathrm{exp}\left\{\left[\mu -\frac{{\sigma }^{2}}{2}\right]t+\sigma \sqrt{t}{Z}_{t}\right\}$ (4)

$\begin{array}{c}Q=prob\left[\mathrm{ln}{V}_{0}+\left(r-\frac{{\sigma }^{2}}{2}\right)t+\sigma \sqrt{t}{Z}_{t}\le \mathrm{ln}DP{T}_{t}\right]\\ =prob\left[{Z}_{t}\le -\frac{\mathrm{ln}\frac{{V}_{0}}{DP{T}_{t}}+\left(r-\frac{{\sigma }^{2}}{2}\right)t}{\sigma \sqrt{t}}\right]=N\left(-{d}^{*}\right)\end{array}$ (5)

KMV将 ${d}^{\text{*}}$ 定义为违约距离(DD)，即资产价值最终分布的均值与违约临界值之间的距离是资产未来汇报变准成的倍数。

3. 参数估计

3.1. 公司资产市场价值的设定

${V}_{A}=D+{V}_{s}$ (6)

3.2. 违约点

3.3. 上市公司资产市场价值的波动率

${u}_{i}=\mathrm{ln}{s}_{i}-\mathrm{ln}{s}_{i-1}$ ，其中， $i=1,2,3,\cdots ,n$ (7)

$s=\sqrt{\frac{1}{n-1}\sum _{i=1}^{n}{\left({u}_{i}-\overline{u}\right)}^{2}}$$s=\sqrt{\frac{1}{n-1}\sum _{i=1}^{n}{u}_{i}^{2}-\frac{1}{n\left(n-1\right)}{\left(\sum _{i=1}^{n}{u}_{i}\right)}^{2}}$ (8)

3.4. 无风险利率

4. 实证分析

4.1. 样本选取

Table 1. Industry distribution of sample companies

4.2. 违约距离和违约概率的计算

Table 2. Assets market value and volatility of sample companies

Table 3. Critical point of sample companies

Table 4. Default distance and default probability

4.3. 同类对比

(一) 建材类

Figure 1. Building materials category

Table 5. Financial status of building materials companies

(二) 石油类

Figure 2. Category of petroleum

Table 6. Financial status of oil companies

(三) 旅游类

Figure 3. Tourism category

Table 7. Financial status of tourism companies

(四) 房地产类

Figure 4. Real estate category

Table 8. Financial status of real estate companies

(五) 同类对比小结

4.4. 类间对比

Table 9. Comparison results between categories

5. 结论

Measurement and Empirical Analysis of Listed Companies Debt Default Probability via KMV Model[J]. 统计学与应用, 2019, 08(01): 6-17. https://doi.org/10.12677/SA.2019.81002

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18. NOTES

*通讯作者。