A contagion model with Markov regime-switching intensities

We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ＇change of measure＇ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps （CDSs） on two underlyings.     

债券违约是否存在区域传染？——基于中国债券市场融资成本视角

2018年以来中国债券市场违约规模攀升,累计违约金额超2900亿元。债券违约后的负面影响受到投资者、发行人乃至监管部门关注。本文以北京、上海、辽宁等八个辖区为例,选取2016~2019年债券违约及债券发行数据,通过构建违约事件对债券发行价格影响因素模型,分析了债券违约的区域传染效应。研究发现:债券违约引发的信用风险存在区域传染性,主要体现为债券发行前若发行人所属辖区存在违约事件将推升债券融资成本;区域内的传染效应与违约时间距离负相关,当时间距离增长时,传染效应变弱,甚至消失;债券违约风险对不同性质企业的传染效应不同,民营企业受影响尤为显著。     

基于担保的中小企业融资的集合票据的定价研究

在简约化模型框架下,考虑担保机构的违约对集合发债融资的中小企业有违约传染的影响,通过引进一个几何双曲线衰减函数,得到了集合票据的定价公式,在此基础上对担保集合票据所隐含的信用风险进行分析.结果表明:担保机构的存在能显著降低集合票据的信用利差,提高其市场发行价格;且有担保下,担保机构的违约传染风险因子越大,相应的集合票据价格就越低,违约概率越大,信用利差越高,担保价值越低.     

关于双曲衰减的违约相关模型及CDS定价

引进一个双曲类型的衰减函数来表示一方违约对另一方违约强度的影响．若交易双方为竞争对手(合作公司),当一方的违约时,另一方的违约强度将减小(增大)．随着时间的推移,这种影响将逐渐减小,直至为零．在这个模型下,通过测度变换,可以得到两公司违约时间的联合分布及各自的边际分布,从而可以对违约互换进行定价．     

A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities

In this paper, we consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes that the intensities of the default times are driven by macro-economy described by a homogenous Markov chain and that the default of one firm may trigger a positive jump, associated with the state of Markov chain, in the default intensity of the other firm. The intensities before the default of the other firm are modeled by a two-dimensional regime-switching shot noise process with common shocks. By using the idea of “change of measure” and some closed-form formulas for the joint conditional Laplace transforms of the regime-switching shot noise processes and the integrated regime-switching shot noise processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we can express the single-name credit default swap (CDS) spread, the first and second-to-default CDS spreads on two underlyings in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.     

利用传染模型对含有对手风险的信用证券定价(英文)

本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.     

Unilateral counterparty risk valuation of CDS using a regime-switching intensity model

We consider the unilateral credit valuation adjustment (CVA) of a credit default swap (CDS) under a contagion model with regime-switching interacting intensities. The model assumes that the interest rate, the recovery, and the default intensities of the protection seller and the reference entity are all influenced by macro-economy described by a homogeneous Markov chain. By using the idea of “change of measure” and some formulas for the Laplace transforms of the integrated intensity processes, we derive the semi-analytical formulas for the joint distribution of the default times and the unilateral CVA of a CDS.     

跳-扩散过程下具有目标杠杆比率的违约风险模型

本文在研究公司债务违约风险时,假设公司价值的动态变化服从跳-扩散过程;假设公司可以根据公司价值的变化调整其债务水平,因而存在公司的目标杠杆比率,违约边界定义为公司历史价值的对数加权平均;当公司价值下降到违约边界时发生债务违约.数值模拟表明公司债务的信用利差对公司的目标杠杆比率和跳过程的强度具有高度的敏感性.本文的模型解决了在长期和短期信用利差预测时结构化模型和约化模型存在的缺陷.     

信用传染违约Aalen加性风险模型

本文考虑了基于加性风险模型的信用风险违约预报模型,不但考虑了宏观因素和公司个体因素,并且通过引入行业因素来刻画公司间可能存在的不同于宏观因素的信用传染效应,由此克服了以往模型对违约相关性的低估.本文在参数加性风险模型下给出极大似然估计及渐近性,提出两种估计方法并比较二者表现,得到最优权估计更加有效.同时本文还考虑了半参数的风险模型,并基于鞅的估计方程得到其估计及渐近性,均得到不错的结果.     

A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach

Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided.     

The loss given default of a low-default portfolio with weak contagion

In this paper we study the loss given default (LGD) of a low default portfolio (LDP), assuming that there is weak credit contagion among the obligors. We characterize the credit contagion by a Sarmanov dependence structure of the risk factors that drive the obligors’ default, where the risk factors are assumed to be heavy tailed. From a new perspective of asymptotic analysis, we derive a limiting distribution for the LGD. As a consequence, an approximation for the entire distribution, in contrast to just the tail behavior, of the LGD is obtained. We show numerical examples to demonstrate the limiting distribution. We also discuss possible applications of the limiting distribution to the calculation of moments and the Value at Risk (VaR) of the LGD.     

Copula方法与相依违约研究

目前信用风险研究的重点已经从单笔债务的违约概率研究转移到多笔债务的相依违约(Dependent Defaults)研究。Copula方法是研究相依违约的重要方法。这种方法是最近几年才被应用到信用领域研究中的一种新方法。本结合代表性献对Copula方法在相依违约研究中的应用进行了探讨。探讨的内容包括Copula方法被应用于相依违约研究的原因、该方法对于相依违约建模理论的改进以及在实证应用中使用Copula方法应该注意的问题。     

Copula理论在信用风险研究中的应用

信用风险研究足近些年来金融数学中的一个崭新的研究方向.本文主要研究了组合信用风险中的常用方法:违约相关性的Copula方法.本文建立了Copula方法与违约相关性研究中的结构化方法和约化方法的联系.此外对于单个公司的生存概率的研究,本文给出了不同于Lando (1998)的求解和证明方法,而这种方法不需要在现在就知道将...     

Credit spreads, endogenous bankruptcy and liquidity risk

In this paper, we consider a bond valuation model with both credit risk and liquidity risk to show that credit spreads are not negligible for short maturities. We adopt the structural approach to model credit risk, where the default triggering barrier is determined endogenously by maximizing equity value. As for liquidity risk, we assume that bondholders may encounter liquidity shocks during the lifetime of corporate bonds, and have to sell the bond immediately at the price, which is assumed to be a fraction of the price in a perfectly liquid market. Under this framework, we derive explicit expressions for corporate bond, firm value and bankruptcy trigger. Finally, numerical illustrations are presented.     

The network structure and systemic risk in the global non-life insurance market

This paper contributes to the literature on systemic risk by assessing the systemic importance of insurers in the global non-life insurance market. First, we estimate the bilateral reinsurance claims matrix using the aggregate outstanding reinsurance data from ISIS and theoretically analyze the interconnectedness in the global reinsurance network using network indicators. The robustness of the estimated matrix is fully assured by sensitivity analysis. Second, we theoretically analyze the contagious defaults introducing the Eisenberg–Noe framework. Reinsurers play a dominant role in the reinsurance network and most of them are included in our data sample. The network analysis finds that some reinsurers with large centrality measures are central in the hierarchical structure of the network. The default analysis shows the occurrences of many stand-alone defaults and only one contagious default via the global reinsurance network after the global financial crisis. In addition, one stress test based on a hypothetical severe stress scenario predicts a few occurrences of contagious defaults in the future. It follows from these analyses that systemic risk via the global reinsurance network is relatively restricted in the global non-life insurance market. In conclusion, our methodology would help supervisory authorities develop an assessment approach for interconnectedness in the global reinsurance network and aid the implementation of insurer stress tests for default contagion.     

基于最优负债系数的上市银行违约概率测算模型与实证

当上市银行的长期负债系数γ的取值不同时,应用KMV模型测算出的银行违约概率大相径庭。根据债券的实际信用利差可以推算出上市银行的违约概率PDi,CS,根据长期负债系数γ可以运用KMV模型确定上市银行的理论违约概率PDi,KMV。本文通过理论违约率与实际违约率的总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型的最优长期负债γ系数;通过最优长期负债系数γ建立了未发债上市银行的违约率测算模型、并实证测算了我国14家全部上市银行的违约概率。本文的创新与特色一是采用KMV模型计算的银行违约概率PDi,KMV与实际信用利差确定的银行违约概率PDi,CS总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型中的最优长期负债γ系数;使γ系数的确定符合资本市场利差的实际状况,解决了现有研究中在0和1之间当采用不同的长期负债系数γ、其违约概率的计算结果截然不同的问题。二是实证研究表明,当长期负债系数γ=0.7654时,应用KMV模型测算出的我国上市银行违约概率与我国债券市场所接受的上市银行违约概率最为接近。三是实证研究表明国有上市银行违约概率最低,区域性的上市银行违约概率较高,其他上市银行的违约概率居中。     

违约强度由Lévy从属过程驱动的约化信用风险模型及信用违约互换的定价

本文引入一个约化信用风险模型,其中违约强度定义为从属过程,即非负增Lévy过程.用概率方法得到了违约时间分布的解析表达式.利用该解析表达式,给出了该信用风险模型下的信用违约互换(Credit Default Swaps)的闭形式的定价公式.     

A Multivariate Regime-Switching Mean Reverting Process and Its Application to the Valuation of Credit Risk

In this article, we study the counterparty risk on a credit default swap (CDS) and the valuation of a first-to-default basket swap on three underlyings under a common shock model with regime-switching intensities. We assume that the defaults of all the names are driven by some shock events, whose arrivals are governed by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of the CDS contract with and without counterparty risk and the spread of the first-to-default basket swap on the three underlyings.     

Joint survival probability via truncated invariant copula

Given an intensity-based credit risk model, this paper studies dependence structure between default intensities. To model this structure, we use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. Through very lengthy algebra, we obtain explicitly the joint survival probability of the integrated intensities by using the truncated invariant Farlie–Gumbel–Morgenstern copula with exponential marginal distributions. We also apply our theoretical result to pricing basket default swap spreads. This result can provide a useful guide for credit risk management.     

债务抵押债券定价中的违约相依性研究

如何衡量违约风险乃至违约相依性是债务抵押债券定价的主要问题.运用PairCopula刻划信用资产组合违约时刻的相依结构,通过Pair Copula分解得到资产组合违约时刻的联合密度,利用Monte Carlo模拟估算CDO各系列的公平价差,进而分析各系列公平价差对回收率的敏感性.实证研究结果表明,Pair Copula能有效捕捉信用资产组合的违约相依性,各系列公平价差随着回收率的增加而减小.