Page 36 - CCFA Journal - Ninth Issue

风险管理 Risk Management 加中金融

Structured Credit Risk Modeling: Merton and Beyond

结构化信用风险建模：Merton 模型的衍生与应用

【作者及翻译】

Eugene Yuqing Wang, Co-founder of CynoRisk Analytics Inc., The Fields Institute for Research in Mathematics Sciences

Huaxiong Huang, Professor, Department of Mathematics and Statistics, York University, Co-founder of CynoRisk Analytics Inc., The
Fields Institute for Research in Mathematics Sciences

Summary
In this paper, we review the literature on the structured credit modeling and its latest development and applications in the risk
management and risk capital charges. The Merton model and other asset process based structured credit models are presented in
three application fields, which are PD models, PD projection models, and default correlation models. Two latest Merton model
industry applications, climate transition risk and DRC IMA model in FRTB, are discussed.

概括
在本文中，我们回顾了关于结构化信用建模的文献及其在风险管理和风险资本方面的最新发展和应用。 默顿(Merton)模型
和其他基于资产流程的结构化信用模型分别在三个应用领域提出，即 PD 模型、PD 预测模型和信用违约相关模型。讨论了
两个最新的默顿模型行业应用，气候转型风险和交易账簿基本审查 (FRTB) 中违约风险(DRC) 内部模型方法 (IMA) 模型。

1 Introduction

Credit risk, which is the risk that an obligor does not honor his payment obligation, is the most important and the material risk in
the financial system. The credit risk is measured at both the individual obligor and portfolio levels, with the most important
measurements being the probability of default (PD), loss given default (LGD) and exposure at default (EAD); and default correlation.
Credit risk models can be divided into two main classes: structural and reduced form models. Structural models are used to calculate
probability of default based on the value of its assets and liabilities. In the reduced form model, or default intensity models, the
default of an obligor is modelled as a Poisson process.

The first structural model was proposed by Merton in 1974 [1]. In the Merton model a company’s equity is modelled as an option
on the assets of the company. It provides a way of relating credit risk to the capital structure of a firm and the probability of default
can be computed via Black-Sholes-Merton option valuation model.

The concept of modeling credit risk via a call option of an asset process has been expanded and become fundamental in credit risk
modeling with the applications in asset pricing, risk capital charges (from Basel 2 to Basel 4), PD projection and stress testing and
credit provisioning in accounting (IFRS 9), climate change transition risks. The paper is organized as follows: in Section 2, the Merton
model is introduced. In Section 3, the extension of the Merton model and their applications in three fields: 1) implied PD and
migration model like Moody’s KMV and CreditMetrics (section 3.1), PD projection models with application in stress testing and IFRS
9 are discussed (Section 3.2), and default correlation models with application with applications in credit portfolio management
(Section 3.3). In the Section 4, the latest development of the application of structured credit model in modeling climate risk and
Default Risk Charge (DRC) Internal Model Approach (IMA) in Fundamental Review of the Trading Book (FRTB) are discussed. A multi-
factor default correlation model that are in compliance with FRTB requirements is presented.

1 简介

信用风险，即债务人不履行其支付义务的风险，是金融体系中最重要、最实质性的风险。信用风险在单个债务人和投资组
合层面进行衡量，最重要的衡量指标是违约概率 (PD)、违约损失率 (LGD) 和违约风险敞口 (EAD)；和违约相关性。信用风
险模型可分为两大类：结构模型和简化模型。结构模型用于根据其资产和负债的价值计算违约概率。在简化形式模型或违
约强度模型中，债务人的违约被建模为 Poisson 过程。

第一个结构模型是由 Merton 于 1974 年提出的[1]。在 Merton 模型中，公司的股权被建模为公司资产的期权。它提供了一
种将信用风险与公司资本结构相关联的方法，并且可以通过 Black-Sholes-Merton 期权估值模型计算违约概率。

通过资产过程的看涨期权建模信用风险的概念已经扩展并成为信用风险建模的基础，应用于资产定价、风险资本金（从巴
塞尔协议 2 到巴塞尔协议 4）、PD 预测和压力测试以及信用会计准备金 (IFRS 9)，气候变化转型风险。
本文结构如下：在第 2 节中，介绍了 Merton 模型。在第 3 节中，Merton 模型的扩展及其在三个领域的应用：1) 隐含的 PD
和迁移模型，如 Moody's KMV 和 CreditMetrics（第 3.1 节），讨论了 PD 预测模型在压力测试和 IFRS 9 中的应用（第 3.2
节） ，以及违约相关模型在信贷组合管理中的应用（第 3.3 节）。在第 4 节中，讨论了结构化信用模型在气候风险建模中
的应用以及交易账簿基本审查 (FRTB) 中违约风险(DRC) 内部模型方法 (IMA) 的最新发展。提出了符合 FRTB 要求的多因素违
约关联模型。

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