可违约零息债券风险综合度量模型研究

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浙江财经学院硕士学位论文

摘要

商业银行交易账户和银行账户中的风险头寸、各类可违约债券、场外投资组

合和信用衍生品等等，可视为违约型金融工具或者可违约资产。可违约资产或组

合同时面临着市场风险和信用风险，在 ERM 模式下，我们应该对这两类主要风

险作全面的管理，单独考虑其中一种风险而忽视另一种，显然不能全面衡量总风

险，尤其是在两类风险都有些许甚至明显作用的情形。然而传统的全面风险管理

模式仅是孤立地考虑不同类的风险，再分别为对应种类的风险提供缓冲资金，这

忽略了不同类风险之间的相互影响效果，大量的研究指出信用风险和市场风险是

相互关联的，所以我们寻求综合风险的度量方法，更全面细致地管理风险。

本文选用最基本的可违约零息债券作为研究品种，其同时面临着信用风险和

市场风险（利率风险），相对于传统的不同类风险独立度量方法，研究风险综合度

量方法，提出了一个可违约零息债券风险综合度量模型，并作出实证分析。

首先，我们分析了可违约零息债券面临的利率风险和信用风险这两类主要风

险，探讨利率风险因子和信用风险因子——违约、违约概率、违约损失率、违约

敞口之间的相互关联的机理。相对于只考虑一种风险的独立度量，也不同于割裂

两类风险再进行加总或通过 Copula 函数关联，我们提出了基于风险强度定价模型

和Monte Carlo 模拟的风险综合度量较为一般化的基本框架，在同一个框架内同

时捕捉可违约零息债券的两类风险。

其次，在信用风险强度定价模型的框架下，我们假设状态过程的两个分量在

实际世界为相互独立的一维 CIR 过程，而无风险瞬时利率和违约强度与状态向量

成仿射关系，允许利率和违约强度相关，并假设风险市场价格的特定形式，建立

了可违约零息债券的双因素强度定价模型。模型的仿射假设不仅很好的体现了市

场变量的特性，还解析地表示出了可违约零息债券的价格、违约概率和模型参数

估计的似然函数。进一步，在风险综合度量的基本框架下和双因素强度定价模型

的基础上，建立计算可违约零息债券综合风险 VaR 的Monte Carlo 方法，得出反

映两类风险的同一个某风险计算期的损失分布和同一个某置信度的损失分布的分

位点，进而能求得风险综合 VaR 值。我们给出了 Monte Carlo 模拟方法具体技术

细节和 Matlab 程序设计，包括违约时间和基础状态向量过程的模拟。

最后，选用作为国内相对真正意义上的信用债券的短期融资券的市场价格和

一周 Shibor 对本文的双因素强度定价模型作出参数估计，估计结果表明违约强度

这个信用质量的统计量和无风险利率的负相关关系，支持了大部分国内外实证研

究的观点。运用本文的风险综合度量模型对短期融资券的综合风险进行计算，得

出风险综合 VaR 值，并与利率风险独立度量 VaR 值和信用风险独立度量 VaR 值

浙江财经学院硕士学位论文

进行比较分析。数值结果表明：相同置信度和风险计算期的综合度量 VaR 值要高

于利率风险独立度量的 VaR 值，也高于信用风险独立度量的 VaR 值，所以忽视一

种风险将在一定程度上低估总风险；随着风险计算期的延长，利率风险所起的作

用减弱，而起主导作用的是信用风险；利率风险和信用风险之间存在着分散化效

果或复杂化效果，所以单独考虑纯粹的利率风险和信用风险，再进行加总既可能

高估也可能低估总风险。

综上所述，本文研究的可违约零息债券风险综合度量模型同时考虑了信用风

险、市场风险和两类风险之间的相关关系，在一个框架内进行建模分析，全面地

衡量了总风险，也为其它类债券、商业银行贷款、场外投资产品、信用衍生品和

可违约资产组合的风险综合度量作好研究的基础准备，有利于全面风险管理技术

的发展。

关键词：风险综合度量；违约强度；仿射过程；Monte Carlo 模拟；可违约零息债

券

浙江财经学院硕士学位论文

III

ABSTRACT

Risky positions in trading and banking books of commercial banks, defaultable

bonds, over-the-counter portfolios, credit derivatives and so on can be treated as

default risk related financial instruments or defaultable assets, and defaultable asset or

portfolios face market risk and credit risk simultaneously. Under the ERM framework,

we should manage overall or comprehensive risk. If we consider only one type of risk

and ignore the other, obviously, the risk management can not be complete and good,

especially when the two types of risk are both playing important roles. However, the

traditional Enterprise-wide Risk Management treats types of risk separately and the

necessary amount of economic capital is determined for each risk type, neglecting the

relation of the two types of risk. Recently, however，a large number of studies have

indicated that the credit risk and the market risk are related with each other, so we

discuss the method of integrated-risk measurement in order to manage the risk more

precisely and in detail.

This paper takes defaultable zero-coupon bonds as the research target, which

simultaneously faces two main types of risk, namely, credit risk and market risk

(interest risk). Contrary to the traditional approach of measuring different risk

separately, we study the integrated-risk and build an integrated risk measurement

model for the defaultable zero-coupon bond. Also, the empirical analysis is presented.

Firstly, we recognize the two main types of risk, that is credit risk and interest risk,

discuss the interaction among the factors of interest risk and credit risk, including

default, rate of loss given default and exposure at default. Unlike considering only one

type of risk or simply adding after measuring different risks separately or the way to

connect the two risk types by Copula functions, we propose a general framework of

integrated risk measurement based on the intensity pricing model and Monte Carlo

simulations, in which the two main types of risk can be captured simultaneously in the

same frame.

Secondly, under the framework of the intensity pricing model, this paper proposes

a two-factor intensity pricing model for defaultable zero-coupon bonds. We assume a

state vector of two independent CIR processes in the real world; also, we assume that

the default-free interest rate and the default intensity are affine functions of the state

浙江财经学院硕士学位论文

vector such that the two are allowed to be correlated with each other. The affine

hypothesis of the model can not only reflect the characteristic of the market variables,

but also give a closed-form pricing formula of a defaultable zero-coupon bond and the

likelihood function for the parameter estimation. Furthermore, based on the general

frame of the integrated risk measurement and the two-factor intensity pricing model,

this paper proposes a Monte Carlo Method of calculating integrated-risk VaR for

defaultable zero-coupon bonds. We find one loss distribution that reflects the two types

of risks in a same risk horizon and one quantile with a same confidence level, so that

the integrated-risk VaR can be obtained. The concrete technical detail for Monte Carlo

simulations and matlab code are presented, including the simulation of default time

and the basic state vector processes.

Finally, we estimate the parameters of our two-factor intensity pricing mode using

the one-week Shibor and the prices of the Short-term Commercial Paper which is

much purer credit corporate bond in our country, and the estimation result indicate that

the default-free interest rate is negatively correlated with the default intensity which

can be regarded as a sufficient statistic for the credit quality. Moreover, we illustrate

the application of our integrated-risk measurement model by computing the

integrated-risk VaR of Short-term Commercial Paper, also, we measure the credit risk

and the interest risk separately and comparatively analyze the VaR values of the pure

interest risk, pure credit risk and integrated-risk.

In conclusion,, this paper study the integrated risk measurement model for

defaultable zero-coupon bonds considering simultaneously credit risk, market risk and

relationship between the two types of risk and measure the total risk in a more

comprehensive way. The research can be a preparation for the integrated risk of other

types of bonds, risky debts of commercial banks, over-the-counter instruments, credit

derivatives and defaultable portfolios and contribute to developing the Enterprise-wide

Risk Management.

Key words: integrated risk measurement; default intensity; affine process; Monte

Carlo simulation; defaultable zero-coupon bond

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摘要：

浙江财经学院硕士学位论文I摘要商业银行交易账户和银行账户中的风险头寸、各类可违约债券、场外投资组合和信用衍生品等等，可视为违约型金融工具或者可违约资产。可违约资产或组合同时面临着市场风险和信用风险，在ERM模式下，我们应该对这两类主要风险作全面的管理，单独考虑其中一种风险而忽视另一种，显然不能全面衡量总风险，尤其是在两类风险都有些许甚至明显作用的情形。然而传统的全面风险管理模式仅是孤立地考虑不同类的风险，再分别为对应种类的风险提供缓冲资金，这忽略了不同类风险之间的相互影响效果，大量的研究指出信用风险和市场风险是相互关联的，所以我们寻求综合风险的度量方法，更全面细致地管理风险。本文选用最基本的可...

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